I don't think you can remake the exact same game but I think if you make a "spiritual successor" where things are different enough to be able to tell that it's not an exact clone of the game, you should be fine.
I've seen plenty of games that resemble a well-known game (e.g. DDR) on newgrounds, but they're all different enough from each other that they're not the same, even if the core mechanic is literally the same.
By "different enough" here, I mean sometimes even changing the art (and/or including art style) and music is enough.
But this is probably erring on the side of caution. I've seen games that were made as parodies of existing games that had almost the exact same art style and so on, and it was fine. Personally I think based on what you described, you should be good, but if you really want to make sure you can PM a portal mod.