First of all, if the game is a flash game, hardware acceleration must be enabled in flash to capture via game capture.
Secondly, if the game in question reverts to going back inside the browser when you alt-tab out of its fullscreen mode, then you cannot capture it via selecting the window in game capture. You must use the game capture hotkey and press the hotkey when the game is fullscreen. Again, however, if flash does not have hardware acceleration enabled, game capture will not be able to capture it.
Thirdly, if it's flash, then perhaps monitor capture may work with it. Most likely one of the captures will probably work.
Fourth, OBS is not perfect, nor do we account for every single type of game on the face of the planet, nor do we have a large team of people to really dedicate time to ensuring that every single game that exists on the planet works 100% perfectly 100% of the time. Sure, it can work, given that you proved that "it can work" because "another application can do it, why can't obs"? But sadly, again, manpower, time, priorities. I wish I could give you everything. I wish I had the ability to fly. But alas, there are always limitations to everything, such as manpower, or in the latter case, physics and reality.
