When Wheeler came up with his idea, antimatter had just been discovered and positrons were the only known form of it at the time. So he was trying to explain why electrons/positrons are so alike, and yet not alike. In other words, just a historical accident that he applied his idea solely to electrons.
But yes, as new antimatter particles were subsequently discovered, his idea could be applied to those as well. In fact, if you're a believer in string theory, one could imagine that there's one fundamental string particle that's moving back and forth through time, creating all the other particles as it does so.