Yikes, that's not an easy question. The original sentence is by far the best-flowing and most neutral, but several of the variations could conceivably be heard. Let's look at them one at a time.
- You all must have played at least once this game.
This is definitely incorrect. The adverb phrase at least once can't break up the verb phrase it's modifying, played this game. It could be placed at the end of the sentence, before the verb (preferably before the auxiliary verb), or even at the beginning of the sentence. As it stands, it appears to be modifying the noun phrase, which is ungrammatical.
- You all must at least once have played this game.
This is acceptable. The less-natural flow makes it sound more formal and puts emphasis on the adverb phrase. I don't necessarily recommend this construction.
- You all must have once played this game at least.
This would be pronounced with a higher pitch on once and de-emphasis on played this game, ending with a rising inflection; the tone of this construction is indignant. This is still not the most natural way to communicate this specific meaning; that would be either the original sentence or #4, each with the same modifications to its delivery.
- You all must have played this game once at least.
As mentioned above, this is a similar but better version of #3. It would only be heard informally, probably after multiple members of the group claim they've never played the game.
- You all once must have played this game at least.
Here we come to our second definitely unacceptable sentence. Once in this position seems to modify must, which is the wrong place for this particular adverb. The possible locations are the same as those given in #1. Breaking up the adverb phrase and putting at least at the end of the sentence sounds both informal and poorly thought out, but it's technically grammatical.