The way the app works seems to me to be a subset of what's required to play Quake well, so if it works I'd bet Quake works better. I also think Quake has other benefits (like reaction time training, spatial awareness, etc, etc) but it could have other downsides too.
A hunch about the benefits of Quake is fine. But, elevating that to a status of belief in such short order seems a little wacky, even if you turn out to be right.