In the case of this specific conversation, it's kind of hard to tell.
You've done the thing most people do - all of us, really, at some point. Which is to try to connect with someone by relating to what they're saying, instead of focusing on their experience.
For instance, people will say things like:
Person A: "I'm seeing Cher in Vegas next month!"
Person B: "I saw her three years ago - she's amazing!"
Instead of saying something like, "Oh really?! Amazing! Are you going to stay in Vegas for a holiday too?" then adding in that they went to see Cher a few years ago too.
It's normal. We want to relate to each other and show similarities. But we often forget to go deeper and actually ask questions in the moment. It doesn't always mean the person is self-centred.
That being said - I've had friends and partners before who did this ALL the time. Not asking questions, making everything about themselves. Just generally not showing much curiosity or actual interest. And I can't vibe with people like that, so I eventually cut them off. Or I put them in a certain "box". For instance, I'm friends with my neighbour, and she's great for drinks and dancing. But whenever we've had lunches or longer hangouts that are centred around talking, she glazes over when the conversation turns to me, and constantly turns the conversation back to herself.
So yeah. In that conversation, I don't see a huge problem. Could be any number of reasons she switched the topic. But if you generally feel a lack of curiosity and interest from her, then maybe review where you want her to be in your life?