In defense of their owner, they did notice what was happening, were appropriately mortified, and cleaned up the mess before hurrying away. Security was notified, but nothing was done, as I saw that same chihuahua in the Artist Alley several more times. I recognized it because it had lettering on its harness that said, "Emotional Support Villain" (hence the title).
Anyway, I've been paranoid of service animals at cons ever since. I understand their importance to people's mental health and wellbeing, but they need to be sufficiently housebroken to not relieve themselves in the middle of a crowded Artist Alley. It's a potential health hazard, it's not fair to the con center or the cleaning staff, and it can't be good for any cosplay that has a long train.
Also, special thanks goes out to my friend Haley Rivers for providing the punchline. When I told my Discord channel about the incident, that was their response.
Rock on, guys, and never stop drawing.