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OK, I see. You had me confused by the terminology you use: normally a Chess Engine means a program that thinks up Chess moves, without any graphical capabilities. It just prints as text what it wants to play, like 'e2e4'. It seems that what you want is not an engine at all, but a Graphical User Interface. So one should not modify a Chess engine, but a GUI like WinBoard or XBoard. It seems it would require a pretty invasive change, though, because such GUIs are of course based on the idea there are two players.

It also seems you don't just want a GUI for local play, but really an internet client that connects to a remote site (e.g. embedded in an internet browser), so that people could play against each other over the internet. This begs the question whether you would want to support 'live' (i.e. real-time with running Chess clocks) or turn-based games (i.e. like correspondence Chess).

About your statement that the game ends as Chess: what if the two surviving parties were neighbors? I suppose their Pawns would move at right angles then. That doesn't seem much like a normal Chess game to me...

BTW, there do exist plenty of two-player Chess variants that end in perfectly normal Chess. For instance Seirawan Chess. Most variants that contain just a limited number of unorthodox pieces on an 8x8 board would turn into normal Chess when these pieces get traded out of the game.