What he said matters. He likes you, he enjoys you, but he’s also putting a ceiling on things early. When someone says they don’t want to think about the future and doesn’t want expectations, that’s usually them saying they want the benefits of a relationship without the weight of one.
Two months isn’t too soon to know if you’re open to building toward something. He doesn’t have to be talking marriage, but hesitating to even call you his girlfriend says something. Especially at 32.
He’s not a bad guy. He’s just being honest about where he’s at. The real question is where you’re at. If you’re falling for him and want something that’s growing forward, staying in this gray area will probably hurt more over time.
Don’t rush to leave. But don’t talk yourself out of what you want either.