But then again it was going to be just that, like this first ever ut review showed:

"more of a mod pack" that version was 221 internally. Basically somewhere between the expansion pack and standalone game idea, this was more like a separate addon pack bundled with the game, hence "unreal tournament edition" ideas originally. I suppose Epic then took this as a base to overhaul the game further, these reactions and to compete with Q3 fully, as opposed to just "more unreal". Its sometimes sad and amazing at same time how competition drives those changes.
I'd just personally call all these inbetween UE1/UE2 versions just the Warfare engine and that's it. That's how it was called before the term UE2 existed. And to me that includes the mobile forces, the unreal 2 e3 alpha and the utxbuild, even though as you pointed out the render in utx is closer to actual UE2.