Earlier quoted context omitted.
Isn't that just relativistic quantum field theory?
that's the thing, gravity from GR doesn't quantize well, or actually at all.
Einstein gravity quantizes remarkably well in the weak field limit; it's called perturbative quantum gravity, and is considered (with good reason) a sound effective field theory (in the Kenneth G Wilson sense of "effective"). One of the results of perturbative quantization is the discovery of the non-renormalization -- by power-set counting -- of gravity and why (very roughly and simply, it's because gravity is a long-range and self-interacting force). However, this only matters in systems where you would need to use Feynman diagrams involving multiple loops of gravitons, which essentially defines strong gravity, and you'll only find that well inside the event horizons of black holes, or in the extremely early big bang universe.
Outside the strong gravity limit, perturbative quantization of Einstein gravity exactly corresponds with General Relativity, as indeed any theory seeking to extend or replace General Relativity pretty well must (since GR accords with so much observational and experimental evidence).
There is also little reason to expect that we will never arrive at methods other than power-set counting to deal with the explosion of variables in many-loop systems, although that in itself should not preclude investment in other quantum gravity programmes that are very different.