I played the game for about 15 minutes, and it kicked my butt to be honest :)
I think it's a compelling core concept for a puzzle game, and I don't think you'll need to worry too much about it being like the one you linked as long as you develop it a bit further. Here are my initial thoughts. I know it's an early prototype so some of this may be on your radar already, but I'll list everything that came to mind just in case.
- Reset button - I found myself wanting to be able to clear the puzzle and start over, especially once I learned exactly which spaces my clicks affected.
- A diagram showing new players which spaces you activate - I think you could pull this off with just one image and little explanation, and it would save a few seconds of confusion at the start of the game. It could be a nice touch.
- Level select - I can see this being useful for people who nail down a strategy for the earlier levels. Since there's no RNG, they would basically end up doing the exact same thing every time for those levels anyway. You mentioned you plan to randomly generate levels which may change the usefulness of this, but I'm not sure in what form you mean to do that, so I'll keep this point anyway.
- Visuals - If you want to distance yourself from that other game, I wouldn't use green as your primary color. It might be cool to allow the player to pick the color scheme actually, or you may find you can do some cool stuff with a completely different visual style.
- Dead Spaces - Instead of only having square grids, you can mix it up by adding dead spaces within the grids. I could see this being the simplest way to vary the gameplay.
Here are the more out there ideas that I don't know would even work, just because you want things that might make it stand out.
- Mirrored puzzle - I'm not sure if this would work, but maybe you could have 2 grids that both register a click at the same spot, but one affects diagonal spaces or something. It would probably be impossible to solve that, but if not it would be an interesting challenge. Maybe there would be some other type of dual puzzle that would work.
- Increased radius - You could include a level where the area your clicks affect is increased to some extent
- Sensitive spots - Kind of an extension of the last one, but maybe there's a special tile that lights or darkens other tiles whenever you hit it.
The only final note I'd have is on the idea of randomly generated levels. Looking at that wikipedia article, if you're thinking of making your levels generate like in that game you'll want to be careful not to allow the game to generate impossible puzzles. Perhaps you can use the math in that article to check each generated puzzle and make sure it's solvable before presenting it to the player. Deviations in how the puzzles are built or solved may also complicate this further, so I'd be careful to always be sure that a puzzle is solvable.