So after a few tries, I managed to light it!... wow this is fiddly :D ! Click once to grab the matchbox, drag it to the fireplace, and click again (the hitbox sucks! for me it worked when I pointed the match itself to the lower-right corner of the fireplace, near the log).
I hadn't played this since the GGJ, 2 years ago, I don't know what we were thinking with the interactions with the dragging, but this is _not_ very friendly.
I still love the look & feel though :), and the lighting! Be sure to turn off the lamp once you light the fire, it's cosier.