No it's not built on their blockchain. But, it does use the Oxen Service Node network (essentially master nodes), which are the nodes that power the oxen blockchain. So, it does use the oxen network, just not the actual blockchain part of it.
Then they also have Lokinet, which I don't know too much about but, I think it's more akin to Tor? That's supposed to get integrated into Session sometime down the road too.
My favorite thing about Session compared to other similar apps though, is that you dont have to give away a single piece of identifying info to make an account. No phone numbers, emails, nothing.