This app specifically improves clear vision at farther distances, which seems far more useful on a daily basis, especially since a lot of people don't have good vision. Compared to twitch games that only improve reaction time in a very limited practically applicable scope. Considering the small amounts of time investment necessary to get good results, this app seems much more useful than playing quake.
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.