Are we dating or not dating?

I have been seeing this one guy now for around 6 months. He’s taken me out to several dinners, spent Valentine’s day with me, gets me gifts, has introduced me to his inner circle of friends and family. Essentially plays the boyfriend role, the only thing is he hasn’t asked me to his girlfriend.
We got into an argument a few weeks back about one of his friends casually hanging out with me and my friends. He said he didn’t like it and doesn’t want to lose to me. We were talking in person and he breaks down and starts crying telling me how much he cares about me, wants a future together, how’s he’s almost told me he loves me several times (in my opinion that’s him basically saying it) but then he says “we’re not dating though.” I tell him to explain himself.
He tells me that he “worded that incorrectly” and claims that him and I are in a relationship and exclusive except there’s no “label” to it. He claims he wants to be 1000% sure because this is the last relationship he ever wants to be in before marriage. I’m not sure what to think because this whole time he’s made it very clear to me how much i matter to him and it’s evident that he’s not spending his free time with other women because he’s working the entire week and spends his time with me always. I’m not sure if I should ask him about it or let it be.
Are we dating or not dating?
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