He sounds to me like a) he's full of it, and b) he's not functioning properly. I have definitely witnessed instances of what's interpreted as ESTJ flirtatiousness, but it's usually just them trying to be friendly, and they themselves don't realize the implications of how they're acting. An emotionally mature ESTJ will not cheat, I don't think it even occurs to them as an option. The idea that he keeps his girlfriend a secret is pretty surprising to me, in my experience an ESTJ in love has a tendency to bring their significant other up quite frequently in conversation, sometimes to the point where it gets kind of annoying for other people, haha.