How to call a JFrame from another JFrame with different classes

One of the solutions would be to use JDialog , whose This is precisely the purpose when more than one window is needed. The difference is that it will be dependent on your main Frame (even though it is a window too), and has the option to be #.

Another thing, usually when working with classes that represent screens, it is more recommended that you extend from JFrame (or another frame class), so you take advantage of features already written in the class, without having to create a method for encapsulate your variable that represents JFrame .

I modified your class a little, and see how it was, just apply the logic of your game.

Main Class:

import java.awt.*;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import javax.swing.*;
import javax.swing.GroupLayout.Alignment;
import javax.swing.LayoutStyle.ComponentPlacement;

public class Principal{

    private JFrame frame;

    /**
     * Launch the application.
     */
    public static void main(String[] args) {
        EventQueue.invokeLater(new Runnable() {
            public void run() {
                try {
                    Principal window = new Principal();
                    window.frame.setVisible(true);

                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
        });
    }

    /**
     * Create the application.
     */
    public Principal() {
        initialize();
    }

    /**
     * Initialize the contents of the frame.
     */
    private void initialize() {
        frame = new JFrame();
        frame.setResizable(false);
        frame.setBounds(100, 100, 450, 300);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

        JLabel lblPedraPapelOu = new JLabel("Pedra Papel ou Tesoura!");
        lblPedraPapelOu.setFont(new Font("Comic Sans MS", Font.BOLD, 26));

        JLabel label = new JLabel("");
        label.setIcon(new ImageIcon("C:\Users\nelio\workspace\PedraPapelOuTesoura\Imagens\pedra-papel-tesoura-final.png"));

        JButton btnIniciar = new JButton("Iniciar");
        btnIniciar.addActionListener(new ActionListener() {
            @Override
            public void actionPerformed(ActionEvent e) {
                //a chamada da tela modal  
                TelaJogo telaJogo = new TelaJogo(frame, true);
                telaJogo.setVisible(true);
            }
        });
        btnIniciar.setForeground(new Color(0, 204, 0));
        btnIniciar.setFont(new Font("Tahoma", Font.BOLD, 16));

        JButton btnSair = new JButton("Sair");
        btnSair.addActionListener(new ActionListener() {
            public void actionPerformed(ActionEvent arg0) {
                System.exit(0);
            }
        });
        btnSair.setFont(new Font("Tahoma", Font.PLAIN, 16));
        GroupLayout groupLayout = new GroupLayout(frame.getContentPane());
        groupLayout.setHorizontalGroup(
                groupLayout.createParallelGroup(Alignment.LEADING)
                .addGroup(Alignment.TRAILING, groupLayout.createSequentialGroup()
                        .addGap(69)
                        .addComponent(lblPedraPapelOu, GroupLayout.DEFAULT_SIZE, GroupLayout.DEFAULT_SIZE, Short.MAX_VALUE)
                        .addGap(88))
                .addGroup(groupLayout.createSequentialGroup()
                        .addGroup(groupLayout.createParallelGroup(Alignment.TRAILING, false)
                                .addGroup(Alignment.LEADING, groupLayout.createSequentialGroup()
                                        .addGap(79)
                                        .addComponent(btnIniciar)
                                        .addPreferredGap(ComponentPlacement.RELATED, GroupLayout.DEFAULT_SIZE, Short.MAX_VALUE)
                                        .addComponent(btnSair))
                                .addGroup(Alignment.LEADING, groupLayout.createSequentialGroup()
                                        .addGap(61)
                                        .addComponent(label)))
                        .addContainerGap(73, Short.MAX_VALUE))
        );
        groupLayout.setVerticalGroup(
                groupLayout.createParallelGroup(Alignment.LEADING)
                .addGroup(groupLayout.createSequentialGroup()
                        .addContainerGap()
                        .addComponent(lblPedraPapelOu, GroupLayout.DEFAULT_SIZE, GroupLayout.DEFAULT_SIZE, Short.MAX_VALUE)
                        .addPreferredGap(ComponentPlacement.RELATED)
                        .addComponent(label)
                        .addGap(44)
                        .addGroup(groupLayout.createParallelGroup(Alignment.BASELINE)
                                .addComponent(btnIniciar)
                                .addComponent(btnSair))
                        .addGap(29))
        );
        frame.getContentPane().setLayout(groupLayout);
    }
}

GameClass Class:

import java.awt.*;
import javax.swing.*;
import javax.swing.GroupLayout.Alignment;
import javax.swing.LayoutStyle.ComponentPlacement;

public class TelaJogo extends JDialog{

    /**
     * Create the application.
     */
    public TelaJogo(Frame owner, boolean isModal) {
        super(owner, isModal);
        initialize();
    }

    /**
     * Initialize the contents of the tela.
     */
    private void initialize() {

        this.setBounds(100, 100, 328, 298);
        this.setDefaultCloseOperation(JDialog.DISPOSE_ON_CLOSE);

        JButton btnPedra = new JButton("Pedra");
        btnPedra.setFont(new Font("Tahoma", Font.BOLD, 16));

        JButton btnPapel = new JButton("Papel");
        btnPapel.setFont(new Font("Tahoma", Font.BOLD, 16));

        JButton btnTesoura = new JButton("Tesoura");
        btnTesoura.setFont(new Font("Tahoma", Font.BOLD, 16));

        JLabel lblFaaSuaEscolha = new JLabel("Fa\u00E7a sua escolha:");
        lblFaaSuaEscolha.setFont(new Font("Tahoma", Font.PLAIN, 16));

        JLabel lblJogador = new JLabel("Jogador");
        lblJogador.setForeground(new Color(0, 128, 0));
        lblJogador.setFont(new Font("Copperplate Gothic Bold", Font.BOLD, 18));

        JLabel lblIa = new JLabel("I.A");
        lblIa.setForeground(new Color(255, 0, 0));
        lblIa.setFont(new Font("Copperplate Gothic Bold", Font.BOLD, 28));
        GroupLayout groupLayout = new GroupLayout(this.getContentPane());
        groupLayout.setHorizontalGroup(
            groupLayout.createParallelGroup(Alignment.LEADING)
                .addGroup(groupLayout.createSequentialGroup()
                    .addGroup(groupLayout.createParallelGroup(Alignment.LEADING)
                        .addGroup(groupLayout.createSequentialGroup()
                            .addGap(134)
                            .addComponent(lblIa, GroupLayout.PREFERRED_SIZE, 63, GroupLayout.PREFERRED_SIZE))
                        .addGroup(groupLayout.createSequentialGroup()
                            .addGap(90)
                            .addComponent(lblFaaSuaEscolha))
                        .addGroup(groupLayout.createSequentialGroup()
                            .addContainerGap()
                            .addComponent(btnPedra)
                            .addGap(9)
                            .addGroup(groupLayout.createParallelGroup(Alignment.LEADING)
                                .addComponent(lblJogador)
                                .addGroup(groupLayout.createSequentialGroup()
                                    .addComponent(btnPapel)
                                    .addPreferredGap(ComponentPlacement.RELATED)
                                    .addComponent(btnTesoura, GroupLayout.PREFERRED_SIZE, 117, GroupLayout.PREFERRED_SIZE)))))
                    .addContainerGap(10, Short.MAX_VALUE))
        );
        groupLayout.setVerticalGroup(
            groupLayout.createParallelGroup(Alignment.TRAILING)
                .addGroup(groupLayout.createSequentialGroup()
                    .addContainerGap()
                    .addComponent(lblIa, GroupLayout.PREFERRED_SIZE, 21, GroupLayout.PREFERRED_SIZE)
                    .addPreferredGap(ComponentPlacement.RELATED, 118, Short.MAX_VALUE)
                    .addComponent(lblFaaSuaEscolha)
                    .addGap(18)
                    .addGroup(groupLayout.createParallelGroup(Alignment.BASELINE)
                        .addComponent(btnPedra)
                        .addComponent(btnPapel)
                        .addComponent(btnTesoura))
                    .addPreferredGap(ComponentPlacement.UNRELATED)
                    .addComponent(lblJogador)
                    .addGap(10))
        );
        this.getContentPane().setLayout(groupLayout);
    }

}

In this way, clicking on btnIniciar of the main class will display your game screen. If you want the main screen to be hidden when the game screen is open, just modify within actionPerformed :

@Override
            public void actionPerformed(ActionEvent e) {
                //a chamada da tela modal  
                frame.setVisible(false);
                TelaJogo telaJogo = new TelaJogo(frame, true);
                telaJogo.setVisible(true);
                frame.setVisible(true);
            }

The main class can be improved, but not to change its code too much, I just adapted the class TelaJogo .