What is the definition of the Doomcore sound?

In a sense, Doomcore is more "limited" and closer to a template than the other Hardcore and Techno genres.
When you look at Speedcore, for example, it could be a lot of things - 300 BPM mayhem with guitars and screams, or 800 bpm noize, maybe even very fast Gabber stuff with Rave stabs... very varied.
Doomcore does not have that much of a range in tempo and elements.

The tracks usually have a steady, "four to the floor" drum around 120-150 BPM (exceptions exist!).
Unlike the general rule in Gabber, the drums do not have to be overly distorted, and a lot of tracks have "plain" Techno drums, especially among the "Oldschool" Doomcore releases.

Apart from the drums, there is Techno / Rave type percussion. And this is one the defining things that sets it apart: it's groovy. It's danceable. Maybe not in an elated-raver kind of way, but it's not just stuff to mosh around and bang your head to (like Speedcore, for example).

And now the most important thing: in almost every case, there is a dark, grim, "doomy" melody, drone, or ambience.
Traditionally, this has been a few detuned / disharmonic synth sounds; often just 3-4 chords, one for every 4 or 8 beats, and then looped again.
I always felt this put Doomcore close to the non-electronic genre of punk rock, which has a similar "3 chord" scheme going on.

Nowadays, the melody can be anything, though, from wild arpeggios and dark ambient drones to movie-like scores.

And while we're at the movies: often vocals, quotes, sentences, are taken from horror and scifi movies and then added to the tracks. "Demons to some, angels to others".

And this is, essentially, the Doom formula.
A lot of tracks are really "just this". A steady drum at ~140 bpm, sparse hits of percussion, 3 synth tones and scary movie samples.

Yet, despite this "simple" template, this structure gets varied and mutated to the highest degree.
There are "miniature symphonies" using these basic elements. Or there are tracks that add further layers, until it becomes an epic production.
Some add the most distorted drums. Some add vocals by a real singer (or themselves).
Some add elements of EBM / Industrial.
Some add elements of gothic and new wave.

This is part of the dark beauty of Doomcore.
Despite its simpleness at "first glance", it is almost infinitely complex.

Oh, and before we go out completely, let us add one more thing: in 99% of cases, huge, cavernous reverberation and echoes are a must!