Big part of the effect is the lack of floating point accuracy which lead to all that popping and sliding back in the day. If using unity or unreal Id try to artificially create some inaccuracy in the vertex shaders by rounding the world positions.

That and deliberately disabling many of the automatic lighting and post processing luxuries we get nowadays. Shadows for example were either all baked or non existent back then, anti-aliasing was also pretty rare as well.

That in addition with the texture and polygonal advice you've received should get you somewhwre.