Incredibly fun. Moving around is fast and chaotic, and it can be easy to mistakenly go in the wrong direction, but it's like Jet Set Radio in how managing to control that motion makes for some very rewarding and seemingly elegant gameplay, at least until you accidentally fall and die or something. There are no checkpoints besides reaching a boss, although levels are short. It's not too boring (though it can be frustrating) replaying levels after dying, particularly because of how fast paced everything is. The level layout's fairly repetitive among each stage anyway, so playing the same part again isn't all that different from just continuing, besides being further from the goal. That being said, instant death pits can be particularly annoying, and at some points it is easy to accidentally fall into one.
I'm not very familiar with other games with its general gameplay from that era, so I don't know how original it all is, but there are a lot of simple mechanics that work really well together. After killing an enemy, its body remains for a short time, with all the bodies disappearing after a certain amount of time has passed with no new kills (or when every enemy present has been killed, in which case an immensely satisfying animation is played). The number of corpses remaining dramatically affects how much damage you do, which is particularly important for bosses (due to their larger health bar), and because of this, boss fights can go by very quickly with a particularly good combo. Killing enemies is also rushed along by a gauge which fills by killing enemies, but gradually depletes over time and damages you if it becomes empty.
At odds with the main melee combat, a limited stock of shurikens is available too. These mostly just stun enemies, and are very much a secondary weapon, though they can also be used to break targets from a distance, or bring down flying enemies. They add an enjoyable amount of variety to the gameplay, but their lower power means that it's not too punishing to run out (and likewise, they make for a nice low stake reward to try and pick up).
The other form of attack is the very limited magic, which works a lot like in other Shinobi games. It's never necessary to save it for a specific point, and you can sometimes get an opportunity to collect another, so they work as an even better collectable item than the shurikens, and as a bit of a safety net in combat.
Movement is particularly ninja-like, with double jumping, running on walls, and dashing through the air (or on ground) allowing for complex manoeuvres. There's normally quite a bit of room for error in terms of platforming, so there isn't too much precision required. Enemies can be locked onto, and like in other games where that's possible, you can easily lock onto an enemy other than the one you expected and then get disoriented. No real way around that though, but it can happen often when there's a lot of enemies present.
Between each stage is a pre-rendered cutscene telling a not-very-interesting story, but there's a very pure early 2000's look to the cutscenes, and the dub is entertainingly dub-ish, so they're pleasant enough to watch (and can be skipped).
But yeah, probably the best Shinobi game, and Shinobi's one of the best series. So it's very good.

Probably the best version of THPS2. It has the first Pro Skater levels unlocked after you finish the main campaign. However, you'll breeze right through those bonus levels due to the high score goals unchanged from the original game. Manual filled combos which weren't present in PS1 will make short work of those goals.

The big drop penalty from PS2 is still present while playing the PS1 levels. Levels like Downhill Jam will be troublesome to play through because they are very height intensive and you'll bail no matter how high your landing stat is.

It also doesn't contain the soundtrack from PS1, but the Xbox had the feature to play music from ripped CDs, so you could theoretically create a PS1+PS2 soundtrack through those means.