After some fan analysis regarding all instances of canon use, the following two points appear to be self-consistent in the use and application of this potion:
Felix Felicis causes the drinker to have a limited period of good luck, during which they are likely to to succeed in all endeavours in which success is possible.
This is accomplished not through direct application of force or granting the drinker any extraordinary powers, but by inspiring the drinker with a favorable pathway through the circumstances.
So the question, "If two equal wizards played against each other in a game of chance after drinking the same amount of felix felicis of same quality, who would win?" becomes moot.
"Success" for one of them is not possible, and it's entirely through chance that one or the other would come out ahead. It quite possible, though, that the one thing the question doesn't take into account, the desires of the individual players, would make a difference.
For instance, one may merely be playing for money, while the other might be playing for fame. It's quite possible that the outcome of the game could give both of them their desires, even if the game appears to pit the one against the other. If, for instance, the fame desiring champion was influenced by Felix to choose to give the money to the loser before the game started (perhaps because he feels he's cheating?), then both potions could work together to cause the fame desiring one to win, while the money desiring one would feel lucky at the end once the winner privately gave the winnings to the loser - as he merely desired the fame.
Perhaps something outside the game provides an influence. One of them might have some "friends" or relatives who, upon seeing their friend win, would pester them or complicate their lives, and so losing might actually be luckier than winning - though in this case the loser might in fact believe the potion didn't work.
Unfortunately there are too many other influences, and too little known about the potion, to make a good objective answer to this question.
At best the result is undefined.