It really doesn't make sense but the hashtag is supposed to be like the joke is so old it was made during the time of dinosaurs when if there had been people they would've been riding them. It would work better if the first thing he said was actually an old joke and not just a vaguely humorous description of the photos
Edit: Wait I guess "Never lose your dinosaur" is the joke, like it could mean never lose the wild part of yourself etc but here he could literally lose his dinosaur because it's running away. Still not an old joke though