This is a contextual acronym, and neither is incorrect nor misused. It's the same that
fps stands for "First Person Shooter" when you are talking about game genre, and "Frames Per Second" when you are talking about framerates. You simply have to read which one is in use.
p2p for communication is more widely known because it is an older acronym used in a lot of contexts outside of electronic gaming. For payment, it is diametrically opposed to Free To Play, or
f2p, and is a lot more exclusive to gaming. Note that if Pay To Play was
ptp, that would entail a separate conflict with
ftp as File Transfer Protocol, so it's not like there's a "nice" alternative.