John's trait says "After each shootout play...if you have more cards in your had than each other player (individually), John becomes a stud..."
Does "each other player" refer to each other player in the shootout or in the game?
Other rulings on Radcliffe mention that his ability is only relevant during shootouts (although he need not be in the posse) http://forums.pineboxentertainment.com/t/john-aces-radcliffe-his-trait-outside-shootout/3066 (ruling that after the shootout, he returns to his printed card bullet type)
So, it would seem that his trait is a shootout trait and then, logically, only other players involved in the shootout need be considered. It would also seem to be an odd interaction if Radcliffe was weakened by a third player in the game who is not involved in the current shootout. But, the text of the card is not specific on this point.