I love the idea of having mini games, but I'm not sure that the health top-up is the best place for them. I mean, maybe they'd be better off as games played on computers scattered around the level, or arcade machines ala Doom3's chicken punch game.
I think that a 3 reel fruit machine thing would be better for the health refuel - like refuel health while the reels spin, and they stop and give a bonus weapon, extra health, shield etc - but more of a bonus thing than playing a game. I can imagine that it would get pretty tense, hoping for a good bonus item to help you win the game.
If this is like say, Unreal Tournament - I would make a lobby level where people connected can chat, play the mini games etc before starting a challenge.... like a little arcade in a lazer tag place. I think that would be a different approach to these games, more social, more fun that watching a timer tick down before the next round. People might want to challenge individuals to a duel, and the waiting players could watch from the arcade
- that would be cool. Deathmatch FPS games tend not to bother with this stuff but I think they miss a trick. A lot of people out there only want to play multiplayer games with their real friends, or only want to play a few games but chat with other players, and mostly prefer to avoid playing with random trolls. Going for the future sport angle makes sense... lets face it, with the way VR is building speed we'll be playing actual games like this within a couple of decades.
Anyway, my point is that with most social activities like cart racing, bowling, lasertag, airsoft, paintball, quad riding etc there is an area where you wait your turn and spend more money, so why not FPS games too.