Place inside your Editor folder to get a full screen game window. Adapted from: https://redd.it/2lymim

FullScreenPlayMode.cs

using UnityEditor;
using UnityEngine;
using System.Collections;

[InitializeOnLoad]
public class FullscreenPlayMode : MonoBehaviour {
	//The size of the toolbar above the game view, excluding the OS border.
	private static int tabHeight = 18;
	private static int tabOffset = -1; // Try 4 on first launch, -1 on second

	static FullscreenPlayMode() {
		EditorApplication.playmodeStateChanged -= CheckPlayModeState;
		EditorApplication.playmodeStateChanged += CheckPlayModeState;

	}

	static void CheckPlayModeState() {
		if (EditorApplication.isPlaying) {
			FullScreenGameWindow();
		} else {
			FullScreenGameWindow();
		}
	}

	static EditorWindow GetMainGameView() {
		EditorApplication.ExecuteMenuItem("Window/Game");

		System.Type T = System.Type.GetType("UnityEditor.GameView,UnityEditor");
		System.Reflection.MethodInfo GetMainGameView = T.GetMethod("GetMainGameView",System.Reflection.BindingFlags.NonPublic | System.Reflection.BindingFlags.Static);
		System.Object Res = GetMainGameView.Invoke(null,null);
		return (EditorWindow)Res;
	}

	static void FullScreenGameWindow() {
		EditorWindow gameView = GetMainGameView();

		gameView.title = "Game (Stereo)";
		Rect newPos = new Rect(0 - 1, 0 - tabHeight - tabOffset - Screen.currentResolution.height, Screen.currentResolution.width + 2, Screen.currentResolution.height + tabHeight);

		gameView.position = newPos;
		gameView.minSize = new Vector2(Screen.currentResolution.width + 2, Screen.currentResolution.height + tabHeight);
		gameView.maxSize = gameView.minSize;
		gameView.position = newPos; 
	}

	static void CloseGameWindow() {
		EditorWindow gameView = GetMainGameView();
		gameView.Close();
	}
}