I don't think that would work in this case. In that fire, all the fuel was coming up through a well pipe, and by detonating a nuke adjacent to the pipe they were able to crimp the whole pipe closed. But with this crater fire, I don't think the fuel is coming up through a single pipe but rather through the earth itself. Detonating a nuke there would probably make the problem worse, by shattering all the rock and making it even more permeable to the gas already seeping through it.

This animation shows the nuclear pipe crimping effect: https://youtu.be/3kwQfjGnVpw?t=68

Since the USSR tried it in 1979, the nuclear option has failed before! (See: 'Yunkom mine')

https://www.nbcnews.com/news/world/ukraine-s-war-torn-donbas...