It seems to me that you're overthinking things. Plenty of games are entirely "deterministic": Super Mario Bros, Tekken, Doom, etc. Almost all action, adventure, fighting, sports, and shooter games are determined entirely by player skill, with little to no random rolling. The only time randomness enters into these games is in computer AI decisions, but even that can be rather minimal. For the most part, doing the same thing every time will produce the same outcome; the challenge is being smart/fast enough to always do the best thing in a given situation. Only RPGs and Strategy games make gratuitous use of random rolls to determine player outcomes, and that seems to be more a nod to their tabletop histories than an important element of their design. So, I'd say yes, of course a game that relies on player skill instead of randomness will work just fine. Plenty of games are and they don't fall apart. Barring chaos theory in regards to atmospheric interference, any sport is largely deterministic.