Gameplay is precisely what I'm recommending it for. I didn't like it the first time I played it, but when I returned to it several years layer, I found it to be one of the better shooters ever, especially when it comes to the semi-realistic category. It has a very good difficulty balance and the check-points do a good job of sustaining a measure of tension: the enemies can kill you fairly quickly if you play poorly and they're quite mobile while also having a number of other basic patterns of behaviour; the areas where larger encounters take place are open, but also divided into smaller paths that make the level design fairly interesting; the player can dispatch the enemies easily if he's accurate, but controlling the recoil takes a bit of skill; finally, the mutants are nicely aggressive and powerful, with attack patterns that are quite unusual for this kind of a shooter.
In many ways it was a prototype for what would later become the infamous Ubisoft bandit camps or whatever they are called, the filler content in their games. I don't think that kind of game occupies a high position within the shooter genre. I'm going to ignore the leaping mutant monkey in the room and how the game goes to hell in a handbasket later on and focus on the combat of the good parts. First off, the guns feel floaty and aren't satisfying to use, it's important for shooters to get this right, and in the case of Far Cry I would say that it absolutely doesn't. Then there are the encounters, you tag enemies from a distance, the stealth is very poor compared to actual stealth games, the map is realistic enough that you don't get much cover and the layouts aren't that interesting, it's too open, which means no matter how you approach the enemy it feels samey. It's not like in F.E.A.R. where you might take a vent to pop up above the enemy, or anything like that. On the other hand the game does not pursue combat sim realism either, it's not Operation Flashpoint, it's not Hidden & Dangerous, it's not SWAT or Rainbow Six. The AI is also broken in that it can easily see you through foliage in the jungle when you can't see them.
I had the opposite curve, I played through the game on release and was impressed, but when I returned a year ago or so it turns out the gameplay just wasn't fun or satisfying. In fact even the jankiest and most half-assed shooters I can think of are higher on my list than Far Cry. I'd rather replay Nitro Family than going through the bland pain of Far Cry again.
It has very little to do with Ubisoft's Far Crys, which can't really be considered to be sequels to the first game in any meaningful way. Ubisoft's FCs are indeed terrible in how they rely on filler content, respawning enemies, and rather a meaningless open-world approach. The original game doesn't have ‘filler’ any more than most other standard shooters have such content, unless you just want to refer to common enemy placement without too much scripting as such. The areas you traverse can't be considered filler content either, as they're all quite distinctive and designed with specific kinds of encounters in mind.
I'd say the weapons are pretty good, actually. The floatiness you're referring to perhaps has to do with how there's a certain amount of sway depending on the amount of movement or the player's stance, which is nice in that you have to put a bit more effort into aiming and how you move, and there's a nice pay-off for keeping focused instead of shooting around chaotically, but on the other hand it is also a nice feature in that there are more stressful situations where you can easily miss a bunch of shots and end up having to take cover or flee. And also, that kind of limitation on the player's accuracy makes more sense because of the size of many areas, where maintaining a pin-point accuracy like in the nineties shooters would just trivialize things. It was also one of the few shooters that required the player to take account of the recoil, which isn't good for all kinds of shooters, but appropriate for this
quasi-realistic, but still fairly ‘casual’ style. The weapons themselves also look pretty nice and sound both powerful and satisfying, depending on the particular type.
The enemy tagging didn't play a big role in the game; you could do it with the binoculars, but the game wasn't insistent about doing it, nor was it that easy to locate and keep track of all the enemies. I do agree about the stealth, though, it's quite awful and non-functional most of the time, and the way the enemies can indeed see you through certain kinds of vegetation compounds the problem. The game certainly isn't without faults. Apart from that, however, the AI is actually quite good (save for the annoying bug when they shoot you without raising their weapons from the idle walking stance).
The open-air maps tend to be quite open indeed, but the shape and type of terrain are very diverse, as is the kind of vegetation growing on it. Combined with rather distinctive camp and larger facility designs, as well as the fact that player is at times given to option to use vehicles, sniper rifles, or take roundabout routes through water or jungle, I'd say there's a considerable variety of approaches; though granted, once the player is within a certain distance of enemies, the combat remains roughly the same. It also has decent indoors areas which are somewhat non-linear and they even some vents on occasion or other places to surprise enemies from. Not that F.E.A.R. doesn't do its own thing well.
When I said that Far Cry is ‘semi-realistic’ I didn't mean to compare it to simulation games, as it certainly isn't one and would benefit nothing from including their mechanics. It rather belongs to that late-nineties-to-early-2000s style of shooters that used realistic weapons, scenarios, and constrained the player's mobility somewhat, as well as making him more vulnerable to damage, but it were still intended to be very accessible and fast-paced.
The encounter design is very similar.
It's true enough that encounters in both games often take place in random huts or larger complexes guarded by mercenaries, which can be approached from multiple directions, but it's all much more loose and interchangeable in Ubisoft's FCs, while the original game has actual hand-crafted level and encounter design.
Edit: Forgot to add that I would also maintain that the mutants are very fun as enemies and they're an indispensable part of the game. They're one of the few instances of tough enemies (in terms of resilience or amount of health) that don't feel like tedious bullet sponges as it is possible to deal with them efficiently if the player chooses the right weapons and has a good aim; but at the same time they also add a fairly unique survival element to the game, and indeed, it's often possible to avoid them and they force the player to approach encounters in a more deliberate way.