It would depend on what the cause of human disappearance was and how quick it was.

The truth is pretty much anything capable of actually rendering humans extinct would probably render most animals extinct humans are far better surviving than most animals are. You talking asteroid impact, solar flare, nuclear war, massive climate change.

Humans can go into shelters, or build mitigation technology. The animals would just die if we didn’t help them.

The only possible way I can imagine that humans would go extinct quickly and not any other life form would be some kind of viral disease outbreak either natural or artificial, but I realistically can’t see something like that wiping out the whole species. You could have a death toll of 10 million people and it wouldn’t even equal 1% of the global population. Especially considering it wouldn’t be 10 million people all from the same area.

Think about all of the things humans have survived and with far inferior technology then anything we have now, ice ages, super volcanoes, global pandemics that keep coming back, hell in the 19th century one of the largest asteroids to hit the world since the extinction of the dinosaurs hit earth and literally no one died or even noticed.