No, traditionally yaoi doesn't need to have sex, just a romantic/sexual relationship between men.
Shounen Ai doesn't really need the guys to have a gay relationship, just a REALLY strong "bromance", and is more a class of shojo manga. In a real shounen ai, you're lucky if the characters ever hold hands. Considering the fact that the characters just made out, this is totally yaoi.
I do get the confusion though, since starting a couple years ago, many non-explicit yaoi (usually webcomics) started being mistagged as shounen ai.
I don't mean to sound rude, it's just a pet peeve of mine that non-sexual yaoi is tagged as shounen ai.
Lolcatz is right, so is our translator aaaand the later volumes go further it's "just" slow burn, not the usual immediate sex thing!
patience, young padawan
Yaoi requires sex (at least some groping). So far it hasn't even come close. This story is still firmly in the Shounen Ai section.