Easy to pick up and play in short bursts. Tons of replay value; a year after purchase, I still go back to it.
Simple controls are essential on the PSP. You don't want a game that's too fancy and gives you a hand cramp because you're trying to simultaneously hold down L1+R1 while steering with your left hand and pressing X and O with your right. The PSP just isn't ergonomically designed enough for that kind of finger-twisting madness. HSG:OT rarely requires more than one button pressed at a time, and hitting a ball takes only some aiming with the control pad, then three taps on the X button. It's simple and elegant.
Autosave is another critically important feature in a PSP game. Save interfaces are normally just interruptions in the gameplay, and that makes players want to avoid doing it. But if they avoid it too long, then they run the risk of running out of battery life (or having to shut off the PSP, for example on an airplane or in class) and losing all that work. Either way, not having autosave is a lose-lose situation for the gamer. HSG:OT automatically saves after every match, which means that your progress is always up-to-date and you can safely turn off the PSP off at any moment if you need to.
Graphics are also important. The PSP is capable of a lot, and has a gorgeous screen -- you need a game that looks good on it. HSG:OT doesn't have the fanciest graphics in the world, but what it does it does well. Backgrounds are nicely blurred, characters are rendered with sufficient polygons, and you never see any unexpected jaggies. There's nothing to break the spell; you are on a golf course.
Sound is important in an interesting way. HSG:OT defaults to just offering simple noises: a bit of wind, some course-specific ambient background, the thwack of the club hitting the ball, and the occasional comment from your caddy/player/opponent. These sounds enhance the experience, but aren't annoyingly repetitive. You can easily play without sound at all, which I like to do with my PSP. You can also turn on in-game music, which isn't bad but gets a little boring. All in all the sound does pretty much what I want it to do -- it sounds nice, but gets out of the way when necessary.
Short levels are also a nice feature. You can pick up HSG:OT anywhere, play for five minutes, and then put it away feeling that you've actually made some progress. Most of the challenges are nine holes, which fly by pretty quickly. (The fact that your player runs at about 150 mph to wherever your ball has landed helps, and is a vast improvement over real golf.)
Collecting items (and experience) is something that actually works really well on PSP. As long as the game isn't annoying, it gives you incentive to go through and play again and again. In HSG:OT you're collecting items to change your character's look -- new hairstyles, clothing, and accessories -- as well as new clubs and balls with different attributes. Doing this is surprisingly addictive, and makes you want to play each level multiple times to get all the items. And as you play more, your character gets better and better with more power, tighter control, and so on. This improvement is another incentive. Essentially, HSG:OT is a perfect model for the collecting game. It's really well done.
And ah, the replay value. I've had HSG:OT for over a year now and I'm just getting around to writing a review. Why? Because lately I've been playing it again. It's easy to just start over from the beginning and play through again. The game is good and the concept is simple -- it's not a movie-like game where you need to follow the plot and once you know the secret it's tedious. It's just golf. When you start over, it takes some time to improve your characters and so on, but you don't really mind that part.
Why? Because it's just golf. And it makes for a really good time. That's all, and that's enough.