I watched half of it. The jumps he makes are impossible unless he's altered the gravity or glitched it or something. He is moving faster than normally possible as well. This is not an out of the box configuration someone is just running through, this appears to be a glitched copy of the game which doesn't really count.
Yes, I was right.
For instance the game featured a mod called Bunnymod Pro "to restore the gameplay to the way it was before the anti-bhop patch back in 2001". Also an enhanced HUD aided the speedrunning. The speedgamers used many scripts including "jump spam, duck spam, 180º turn for gauss boost and precise use-key actions". There are 317 segments in the game with 249 of them under five seconds in duration. The team has even published a spreadsheet on Google Docs showing the gameplay segments and timings.
He's using mods and scripts to defeat normal game mechanics and gameplay. That's not beating the game as it is, that's modifying the game. Doesn't count imho.
Also, where is the tram ride? That's part of the game as well and completely bypassed.
it's called a tool assisted speedrun. i guess you've never ever heard of it, since TAS and regular speedruns are judged separately and there are separate records for each game. train ride is skipped because it's a non-gameplay segment which can't be sped up with any amount of bunnyhopping or movement scripts.
the draw of TAS is that it becomes possible to beat the game along an "ideal" path; as you mentioned, there are many five-second segments to this speedrun: imagine all the time that went into discovering and exploiting all of the glitches that they used, as well as perfecting the application of each glitch to a given gameplay segment. TAS isn't bullcrap like you think it is -- it takes at least as much effort and game sense as a regular speedrun.
in fact, a common tool used in assisted runs is slow motion or incrementing the game state in single frames at a time, applying inputs, and incrementing by another frame. it's like the difference between starcraft and civilization: real-time vs. turn-based. the fanboys on both sides will tell you that the other one is terrible but there's plenty of nuance in each.
edit: of course, there are still rules for tool assisted runs. generally, you can only do things that the player can do in-game aka no game mods, memory editing, or other external tricks. tool assist simply enables the player to play the game at the maximum possible potential within the limits of the player's in-game agency. however, in this case, it looks like he used the bunnyhop patch so that his run could be judged consistently against past speedruns of half-life.