Execution can be a subjective thing. I don't mean to be pedantic, but you'll have to be more specific on whether you mean the mood/atmosphere or the "puzzle" of a specific room, or the combination or the variation of them between rooms, etc. of a specific set piece or all of them combined.
Does execution ever become better than originality and is something still original, if it tricks you into thinking it is, such as by using the same challenge from a different angle?
What I'm getting at, is that execution is a buzzword to cover every design decision of a particular set piece. When I keep mentioning scripted events, that's because it's an easy example that Half-life did exceptionally well - I also imply that they have to be used effectively and not just because; I hope you know that. Scripts such as enemies moving in, things breaking or sounds starting up upon you reaching certain points, that's not only part of execution, but in Half-life that was a near constant occurance to make everything look like a living breathing world that reacted to your presence.
That's meticulous, tangible design that we can point to and distinguish from other games, because designers use less obvious scripted events now and rely more on AI and pathing for you to engage when you want to in a living world. On more than one occasion, you could see soldiers or aliens wait until you walked ahead by a couple of centimeters. You don't see that anymore in big titles, but in reverse you saw that a lot in Quake and Quake 2 if you moved outside the expected path.
Deus Ex (released 2 years later) already improved on the world interaction by not letting anything happen until you screwed up by getting seen or trespassing, or engaged enemies. That's one example of doing something better, though the game was flawed in other ways, such as letting aiming be a skill that you had to level up (making gunplay really hard and unforgiving, almost unnaturally so. A game design choice, but a bad one in my opinion). Another aspect of that was the multiple approaches and open areas used to effect (unlike open areas being the play itself like it is in sandbox games).
When things are done right, players rarely notice these things. When you finish a set-piece in a new game, you're more likely to have already seen everything in it from other games than not. This is where I think the jaded mentality comes from.
As games become increasingly easier as well, you can brute force through everything and don't have to suss out what the developers intended the challenge to be (which I admittedly very rarely do).
When something is done wrong, again DooM 2016, you can pinpoint it though, such as the incessant "hell in a cage" style set-pieces where you can't turn back, but are forced to fight in an unexplored location for a set amount of enemies.
We can just look at new games and state that we hope they have the right execution, but it becomes a nebulous term and doesn't make for a good discussion or argument. That's why I focus on what they'll do that sets the game apart, because I already assume they'll
some sort of execution. From the video that's linked in the top, it seems to be alright, but then again I have to know what specifics you mean to relate it to.
Deus Ex (all of them, even the 2nd one), System Shock 2, Aliens vs. Predator, Red Faction, Painkiller, No one Lives Forever, VTM: Bloodlines, Prey, Bioshock, Dishonored, Wolfenstein (the newest one) and probably a lot more than I can remember are all very good games that in some ways are better than Half-life. If you can't find *anything* you think is better executed in any of those, even in some of the CoD games, bulletstorm or something like RAGE, then I think you might be either biased or too general