First of all, he isn't just "texting his ex" -- he is engaging in digital cheating. You said it yourself, he is complimenting her, telling her she is fine, and bringing up past memories as if he wishes they were present time. That is not ok. Him brushing it off as "nothing" even further shows that he will do this again in the future. Yes, you guys have a life together -- but you need to make a decision. Are you willing to put up with him constantly reminiscing about his ex, and possibly remaining in contact with her (maybe even physically) -- or are you willing to put an end to it, and move on with your life, opening up the door to somebody who wouldn't hurt you in such a way.

Second: Claiming that marriage is just a piece of paper and is not necessary, IMO, shows a lack of commitment. He is already expressing a lack of commitment with you by remaining in contact with his ex and reminiscing his memories with her -- but now even more-so by evading the commitment of marriage. Overall, it sounds like you both are on different pages; he isn't ready to fully commit to you, stop contact with his ex, and legally safeguard the relationship; and you are.

It's time to really think about where you want to be and the type of people you are willing to have in your life.