I'm sure that's what's happening here

I mean, that is a pretty reasonable way to do a mirror, or a very glossy reflective floor (just throw a transparency/alpha layer over it and render it on top of the floor texture) back before... shaders as we know them today really got invented, and model poly count/texture res is not very high... and you specifically only do this kind of mirroring in enclosed, indoor areas that don't have huge vistas.

Like, I don't think Deus Ex is on 'the build engine', but it certainly ultimately derives from it, and it does this.

Then you get to HL2, and while, to my knowledge, HL2 doesn't literally have 'mirrors' in it, you can basically do that by making a render target camera, the kind that displays in the game as a TV screen of some kind... well you could just point that camera right out of where the mirror is, and have the render quality/resolution be lower than the quality/resolution of the rest of the world.

(ofc this wouldn't work in hl2 just per se, because gordon isn't actually rendered as a player model, but you could futz around in gmod not long after hl2 and do this, i know this because i did it)

I am reasonably confident most modern games with mirrors ... basically do that, just with an actual game settings slider to determine fidelity instead of all those settings that used to be baked into the map as it was with custom hl2/gmod/sourcemod maps.

Water, window and world space reflections can/could also be set to just... render the whole world again in a lower quality... but prior to that, it was more common to bake a static 'reflect map' into your compiled map, as realtime duplicating the whole world can often be waaay too demanding.

And of course now we have shifted over to the Real Time Ray Tracing paradigm, that is absurdly high fidelity but absurdly highly demanding, and that has neccessitated the development of frame upcaling and frame gen tech to balance out the performance losses from this absurdly inefficient lighting paradigm.

i think it wasn't until far later than this that any engine was emulating reflections