The PC version of Die Hard was created by Dynamix, a team known for high-concept adventure games that made use of digitized graphics and animation in the days before those were a common thing. They made some very unique games that sometimes pushed technological and creative boundaries, but they were also commonly not very user-friendly and could be hair-pullingly frustrating and clunky. Die Hard for PC is pretty typical of their output in that regard.
The game utilizes a pseudo-3D; I'm pretty sure this is an early version of the engine they would eventually use in Betrayal at Krondor. The view is from directly behind John McClane as he navigates Wireframe Nakatomi Plaza. You mostly comb the plaza trying to follow the plot of the movie while either punching to death or gunning down various Gruber henchmen; you'll need to take key items off their bodies that are then used to replicate some of the movie's iconic scenes, like using a power cord you find early on to later rappel from the roof through a lower level window. These are frequently interspersed with digitized still cutscenes from the movie, though weirdly the likeness of all the actors seems to be included *except* for Bruce Willis. Guess he had a special licensing deal or something.
You move and strafe in the current direction you are facing using the arrow keys, and can switch perspective by holding down the SHIFT key and then pressing in the cardinal direction you wish to turn. When a henchman pops up, you hold SPACE and use the right column of numeric keys for various attacks and the middle column for various dodges and blocks. Tapping SPACE quickly with the gun equipped causes McClain to stop and aim, and you can wave the gun all around in front of you with some amount of precision (though targetting shots is rarely necessary as the thugs always seem to run right up in your face anyway.)
The controls are a bit cumbersome, but actually would probably be tolerable if the game wasn't so glitch-filled. Right from the jump, it seems totally random whether John starts with either one clip or an empty gun. If it's the latter, you might as well quit and restart, as you encounter bandana henchmen right near the start that know some sort of advanced karate and can't seem to be successfully melee'd with. Also, the only reliable way to kill a guy appears to be to punch them up; when you shoot at someone, sometimes they just randomly disappear into the Void. Sometimes they pop back up randomly a few rooms away, but sometimes they're just gone for good, and that's a game-breaker if they were carrying an item you need. Henchmen in the larger rooms are also a bit dopey and seem to not notice you if you're more than a couple squares away from them and walk right by. You can also give many of them the ol' Resident Evil zombie treatment and just run around them and run away; they'll follow you through a couple of rooms but seem to give up after that.
Compounding the frustration here is a very tight time limit of only 20 minutes of real time (seen constantly in the top of the HUD.) You'll likely burn half of that on your first session just coming to grips with all the vagaries of the controls and game engine. The game does provide you with a nice map of each floor highlighting key areas, but as you have to get so many items off of random Gruber Goons, you end up having to roam all over them somewhat randomly anyway searching for all the inventory crap you need. There's also the issue of not really being able to play this on laptops as you need the full numeric pad. Enabling the virtual numeric pad doesn't really help as the game also requires use of hotkeys all over the keyboard like H, F and S. You might be able to cobble out a control scheme in DOSBOX with a bunch of effort but the game really isn't worth it.
Die Hard was released back in the day when a publisher with a movie license would often release wildly different versions of the game for different platforms. Activision also published the NES version of Die Hard at about the same time, which we covered last Xmas
; conceptually it has some similarities, but was handled by a totally different team and actually plays a bit more smoothly.