The most obvious one is AI. These things are incredibly parallel & entirely self-contained, and a consumer desktop PSU could power countless amounts of them without a second thought. At $2,000 for 100 chips ($20/chip), you can start to do some really interesting stuff for the cost of a consumer laptop.
It's natural that AI is a problem this chip excels at, given Moore studied under McCarthy and all.
If you feel morally okay with playing with proprietary software, I really recommend playing a little bit with the simulator of the chip. Given what's intuitive with one or two, you'll probably be able to see the possibilities much better after an hour or so of play.