Agreed on Red Faction, that's the game that really stands out to me as a direct Half-Life "clone", so to speak. As for the others:
Is Halo influenced by Half-Life? Halo boasted of larger and more open maps, plus a focus on vehicles. Neither present in Half-Life.
NOLF is debatable - they no doubt looked to Half-Life for guidance, but Monolith was already trying to make games like that pre-Half-Life. Shogo and Blood 2 feel at times like very poor attempts at doing NOLF.
DNF 2001 build does look very shit, but not in a way that I'd consider Half-Lifey.
MOH:AA is interesting. Again, they probably did look to Half-Life, but it's also kind of codifying its own relatively new genre. Many of the levels are remakes of levels from the original 1999 Medal of Honor, which I assume wasn't heavily Half-Life influenced due to their development times overlapping.
No comment on Turok 3, can't remember any of it.
I'm not sure I could identify any specific lessons or level design tricks RTCW took from Half-Life.
Are these bad games, though? Red Faction is a fun diversion, I think NOLF is typically overrated but it's alright, MOH:AA is good for what it's trying to do, RTCW is fine except for a few standout awful levels. None of those really suggest a negative trend in FPS games to me - most examples of that come after the release of CoD, especially CoD2.
All of those are influenced by Half Life. Influence doesnt mean copy/paste everything. It means imprinting a direction for everyone else and have them take various cues from your game and adapting them to their project. Monolith's entire dirrection at the end of the 90s was due to Half Life. They even mention it:
"
Half-Life confirmed our growing conviction that presentation is more important than innovation:[...]What makes it so influential is that it does everything so well. The pacing is sublime, the situations inventive, the AI incredible, and the overall level of polish unprecedented. It's a game made up of unforgettable moments. Polish, therefore, was our chief mandate. We felt it was better to release a comparatively humble game that got all the details right than an ambitious one that fell short in numerous areas."
Half Life's influence is in everything from Allied Assault to COD all the way to Resident Evil 4, Uncharted and so on. Neil Druckman claimed Half Life was the game that made him want to make games.
Even a game like this indie Silent Hill copy cat takes cues from Half Life, in a way thats not neccesarily obvious: “I’ve tried to take cues from games like Half-Life in the way that Valve uses environment design to naturally develop the narrative,”
https://store.steampowered.com/app/1257030/Heartworm/
System Shock 2
"we realized that our design time and budget were very tight and that we would not have time to carefully hand-script complicated game-play sequences in the engine. Instead, in an attempt to shift the battlefield, we chose to focus on simple, reusable game-play elements. The success of
Half-Life, which launched while we were in the middle of
System Shock 2 confirmed our intuitions in this respect. We simply didn't have the time, resources or technology to develop the scripted cinematic sequences used by
Half-Life. We consoled ourselves with the knowledge that we were not even trying to do so.
Motivated by the dramatic scripted sequences in
Half-Life, we attempted to introduce similar elements into
System Shock 2. In doing so, we broke one of our rules: we tried to step outside the bounds of our technology. Although we attempted relatively simple sequences and ultimately got them working, they were time sinks, and the payback was relatively slight.[...]We confirmed our intuition that the Dark Engine does not support complex scripted sequences well because the toolset (AI, moving terrain, and animation) is not optimized for this sort of behavior."
Like i said, influences are often not in your face or a copy cat game. When Thief 1 was nearing the end of development, devs looked at tha success of Commandos. They considered that game a peer in stealth design. But most people would never associate Commandos with Thief. And then Commandos 2 gets released with a sound mechanic. Wonder where they got it from