this is a sincerely asked question. Have you never played a game of chase where your dog started the game but you were able right in the middle of chasing him, turn it around so that he was exuberantly chasing you?
With my guy, and I don't use the game habitually to do anything other than for mutual fun, or a stress reliever, or just giving him and me a break from routine. I have found that the chase game if manipulated to include my boundaries and an ending signal is a wonderful stress relief game that adds a bit of short cardio.
I have used it to rope my guy in, change his attitude about what I need from him, changed my attitude about what I have to get done with him. I only have my one boy from which my experiences of the game come from but in a handful of chase/tag/keepaway (whatever you want to call it) it has been a powerfully, mutually experienced positive game for both of us once he understood those boundaries. Plus, I do set it up so that I am successful in the game also, i.e. On the deck so I can catch up to tag him and run away. Or in the yard, a stop quickly with the command indicating time to tug or whatever.
In my newbie nutty thought process based only as I have explained,chasing and running away from is innate in them and harnessing it is done all the time for obedience and sports training purposes. The difference is is that for obedience and sports, it is just the use of the very beginning of the chase or run away drive being utilized. The chase game allows for full out use.