The last survey reported that Less Wrongers on average believe that humanity has about a 68% chance of surviving the century without a disaster killing >90% of the species. (Median 80%, though, which might be a better measure of the community feeling than the mean in this case.) That's a lower bar than actual extinction, but also a shorter timescale, so I expect the answer to your question would be in the same ballpark.

Would you say that many people here (and yourself?) believe that the probable end of our species is within the next century or two?

For myself: Yes! p(extinct within 200 years) > 0.5