Navigating out of a TextField in a GridPane using the arrow keys in JavaFX

You need to set the event handler to move on arrow key press as you can see below look at the setTextHandler function there is no error handling I just wrote this up to give you an idea of what you should be doing it is called from the loop when you create the TextFields from there it checks for an arrow key press and from there it will .requestFocus() from the next TextField

public class Main extends Application {

    private TextField[][] squares;

    @Override
    public void start(Stage primaryStage) throws Exception {
        squares = new TextField[9][9];
        GridPane grid = new GridPane();
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                squares[i][j] = new TextField();
                squares[i][j].setPrefHeight(8);
                squares[i][j].setPrefWidth(25);
                setTextHandler(squares[i][j], i, j);
                grid.add(squares[i][j], j, i);
            }
        }
        grid.setAlignment(Pos.CENTER);

        Scene scene = new Scene(grid);
        primaryStage.setScene(scene);
        primaryStage.show();
    }

    private void setTextHandler(TextField textField, int i, int j){
        textField.setOnKeyPressed(keyEvent -> {
            System.out.println(keyEvent.getCode());
            if(keyEvent.getCode().isArrowKey()) {
                if (keyEvent.getCode() == KeyCode.UP) {
                    squares[i-1][j].requestFocus();

                } else if (keyEvent.getCode() == KeyCode.DOWN) {
                    squares[i+1][j].requestFocus();

                } else if (keyEvent.getCode() == KeyCode.LEFT) {
                    squares[i][j-1].requestFocus();

                } else if (keyEvent.getCode() == KeyCode.RIGHT) {
                    squares[i][j+1].requestFocus();
                }
            }
        });

    }
}

To avoid the focused TextField from handling arrow keys at all you need to intercept the KeyEvent before it reaches said TextField. This can be accomplished by adding an event filter to the GridPane and consuming the event as appropriate. If you're not sure why this works you can check out the JavaFX: Handling Events tutorial.

Then you can use Node#requestFocus() to programmatically change the focused node.

I also recommend setting the prefColumnCount of each TextField rather than trying to set the preferred dimensions manually. That way the preferred dimensions are computed based on the font size.

Here's an example:

import javafx.application.Application;
import javafx.geometry.Insets;
import javafx.geometry.Pos;
import javafx.scene.Node;
import javafx.scene.Scene;
import javafx.scene.control.TextField;
import javafx.scene.control.TextFormatter;
import javafx.scene.input.KeyEvent;
import javafx.scene.layout.GridPane;
import javafx.scene.text.Font;
import javafx.stage.Stage;

public class App extends Application {

  private TextField[][] fields;

  @Override
  public void start(Stage primaryStage) {
    GridPane grid = new GridPane();
    grid.setHgap(3);
    grid.setVgap(3);
    grid.setPadding(new Insets(5));
    grid.setAlignment(Pos.CENTER);
    grid.addEventFilter(KeyEvent.KEY_PRESSED, this::handleArrowNavigation);

    fields = new TextField[9][9];

    for (int i = 0; i < 9; i++) {
      for (int j = 0; j < 9; j++) {
        fields[i][j] = createTextField();
        grid.add(fields[i][j], j, i);
      }
    }

    primaryStage.setScene(new Scene(grid));
    primaryStage.show();
  }

  private void handleArrowNavigation(KeyEvent event) {
    Node source = (Node) event.getSource(); // the GridPane
    Node focused = source.getScene().getFocusOwner();
    if (event.getCode().isArrowKey() && focused.getParent() == source) {
      int row = GridPane.getRowIndex(focused);
      int col = GridPane.getColumnIndex(focused);
      // Switch expressions were standardized in Java 14
      switch (event.getCode()) {
        case LEFT -> fields[row][Math.max(0, col - 1)].requestFocus();
        case RIGHT -> fields[row][Math.min(8, col + 1)].requestFocus();
        case UP -> fields[Math.max(0, row - 1)][col].requestFocus();
        case DOWN -> fields[Math.min(8, row + 1)][col].requestFocus();
      }
      event.consume();
    }
  }

  private TextField createTextField() {
    TextField field = new TextField();
    // Rather than setting the pref sizes manually this will
    // compute the pref sizes based on the font size.
    field.setPrefColumnCount(1);
    field.setFont(Font.font(20));
    field.setTextFormatter(
        new TextFormatter<>(
            change -> {
              // Only allow the text to be empty or a single digit between 1-9
              if (change.getControlNewText().matches("[1-9]?")) {
                // Without this the text goes "off screen" to the left. This also
                // seems to have the added benefit of selecting the just-entered
                // text, which makes replacing it a simple matter of typing another
                // digit.
                change.setCaretPosition(0);
                return change;
              }
              return null;
            }));
    return field;
  }
}

The above also adds a TextFormatter to each TextField to show a way to limit the text to digits between 1 and 9. Note the arrow navigation does not "wrap around" when it reaches the end of a row or column. You can of course modify the code to implement this, if desired.

You may want to consider creating a model for the game. That way the business logic is not tied directly to JavaFX UI objects. When you update the model it would notify the view (possibly via a "view model", depending on the architecture) and the view will update itself accordingly.