The Google Chrome Dino game is an endless runner game, but the score isn't exactly endless. When you reach a score of 99999, the score counter simply maxes out. That means the game doesn't stop, but your score doesn't increase anymore.
There's a funny little bug associated with this score: if you manage to reach 99999 points, the pterodactyls (the flying enemies in the game) might disappear from the game due to a bug, making the game easier because you'll only need to dodge the cacti.
Keep in mind that reaching a score of 99999 is quite a challenging feat, as the game speeds up and becomes more difficult the longer you play. It requires a lot of practice and patience to achieve such a high score.