Can I use a fondue bourguignonne set to make cheese fondue?

For a fondue bourguignonne (oil) or Chinoise (broth), raw ingredients are cooked in the pot, which means you need to get the liquid at least close to a boil, i.e. in the 90-100 C range. The burner under your model should easily supply enough heat.

For chocolate fondue, this would mean the chocolate would burn almost instantly. If you serve a chocolate fondue with a heat source at all, you'd use probably a tea light (small candle) at a distance.

Cheese fondue can take more heat than chocolate, but less than broth or oil. The idea is to just keep the warm cheese liquid. If you can reduce the power of your burner a bit, e.g. by closing the outer holes, you should be ok. Just pre-melt the cheese mix gently on the stove, not over the flame of the rechaud and never forget the "stirring rule": each participant is to use his bread on the fork to stir once or so over the bottom, to ensure the cheese doesn't stick. If you use a heavy ceramic pot instead of a metal one, it would be even better, but your set should work, too.