I've been taking a look into this and the last version where recording is possible was 0.13.2 in the Scirra nwjs list, or 0.13.4 if you download it directly from the NWjs website. Unfortunately this version also has a bug where, if the player closes the game, nwjs will still run in the background, which is awful.
Any version after that just won't show up, not only in OBS, but other stream apps I've tried. I've googled a whole lot and it seems to be a bug with how Chrome uses DX11 - but it could be just speculation. One of the workarounds is disabling hardware acceleration, but that will make your game run like complete crap.
This is awful. This bug has been around for not one but two whole years, and apparently no word if it's getting fixed or when.
Edit - It also seems to work with version 0.18.7, using "game capture" instead of window capture. I'm going through some versions right now and testing them.
Another edit - I've ran a few more tests and apparently adding " --in-process-gpu" to the package.json allows the game to show up on OBS, when using the "game capture" option. However, resizing the game window makes the recording freeze and the only solution is to close and open the game again. Still, a pretty good solution! I'm glad I can use the latest version.