But it is the same overall code structure, the same game, etc.
All these oss quake engines, are they quake? Ironwail, quakespasm vkQuake?
Half-Life 2 sure won't play quake maps nor will it play hl1 maps.
Not without modifications but Half-Life: Source is essentially a tech demo to show that they can be ported easily (if you are OK with dropping some pesky features like randomized wall textures).
I see impressive stuff with reimplementations such as Surreal Engine, but they will require far more powerful machines.
If Surreal had a software renderer (not requiring AVX or similar) running under an SSE2 machine, that would yield even more respect, because if your reimplemented engine runs in legacy machines the portability would explode. Just have a look on Scummvm on how many platforms and OSes can it run. Or the Super Mario port for PC, where some fork supports even 3DFX under DOS, and GL 1.2. Thus runnable under TinyGL with no 3D accelerators and even under Plan9/9front with custom tweaks.