Wow! I'm not sure where to begin with this one. I can see why people hold this series in such high regard.
I'll be approaching this from someone who started the Half Life 2 series coming from Black Mesa, so others in the same boat might know what to expect.

First of all
There are some marks of an older game that might be a little frustrating, but understandable when first stepping off Black Mesa.
First, your flashlight and sprint are run off a mechanic called Auxiliary Power, which drains as you use either one, and takes a second to recharge. It was a bit jarring coming off the game where sprint and flashlight were infatuate, but I can understand from the thought of this having more horror elements. As well as a potential lore reason, which is that in this game you don't have the resources of the Black Mesa facility. So your suit doesn't have access to nearly as much power.

Another is that there are times where you may get a weapon or item that you only use once, or the item you're given may not be very clear in how you're suppose to use it.
Example: With out spoiling anything, one of the throwable items you get, really only work if you are around a specific type of enemy, after that, they are basically useless.
Another is a near end game enemy, that seems to have a very specific weak spot, and you can find it if you are paying attention, but can be easy to miss, and waste resources on.

Other then that, the game play is amazing! I can definitely see where Black mesa got its inspirations for its level changes, the chase scenes and combat of this game are crazy exciting for a game that's 20 years old at the time of writing.
Valve uses the physics engine quite a bit in this game too, puzzles and environments make you navigate through them by moving items with the gravity gun, or by figuring out your environment, which is really cool, and makes you take in the whole level, rather then just the path you're suppose to follow.
The weapons are satisfying and punchy, and the combat more or less makes you run into the fray and think on your feet, nothing to the level of Doom Eternal, but enough to where you start to ensnarement and plan out which enemies you'll be taking out in which order.

The horror elements of the game can actually be a little frightening, especially around the half way mark, where you're introduced to a set of new creatures in an environment that is definitely reminiscent of Left 4 Dead.
Making you forget you're badass physicist Gordon Freeman for a bit, and have you looking around every alley way to make sure somethings not going to jump at you. Literally.
It also helps that this level gives you a bunch of saw blades, and not a lot of ammo, giving you a since of gritty dystopian horror that helps with the atmosphere.

The story of the game is honestly really interesting, best described as a 1984 approach to cosmic horror and natural disaster. It has you, Gordon Freeman, waking up from stasis, due to one of the events from the previous game, and finding that the entirety of the human race has been enslaved by a militia of interdenominational Aliens known as the Combine, and has you navigating a familiar world, plagued with this unknown "big brother" controlling the citizens and abusing their power over the humans they've enslaved. They also seem to hold a scary amount of knowledge and power as they use aliens from the last game to frighten, subdue and kill the unruly rabble. They also have enslaved the Vortigaunt, again. I honestly feel really bad for those poor bug eyed buddies.
On top of all this, it seems that what ever otherworldly entities that had a hand in the events of Black Mesa, still have uses for you, Gordon Freeman. You get the constant since that there is much more going on in the back ground of this dystopia, and are given a few mind bending details throughout the game, without ever truly spelling things out for you.

All and all, I can see the hype, the only down sides are the aforementioned dated and jarring elements of the game, and the fact that the story could be mildly confusing at points, but in cosmic horror fashion, that is part of the point of the story its self.
I give it a 3.5 out of 5 for fun mechanics, an interesting story and fun combat, but the lack of music in certain parts, the confusing nature of parts of the story, and single use or difficult to understand tools leave a bit to be desired. Good thing there are still 2 more games! I can;t wait to see what's in store.