> how is this done ?? what engine is used ? it feels exactly like the original

It's most likely using reVC, a reverse-engineering of the original binaries by decompilation, and then built for the web using emscripten, which does a fairly good job making OpenGL code work on WebGL.

My Tomb Raider web build I linked here elsewhere was done the same way (reversing by the amazing people in the TR1X project).

Pro tip: press R for free roam script in menu. This was a debugging feature in re3 and reVC.