In what way, honestly? Other than, "My guy is simple to run and uses a two-handed sword?"
Well, when you played a fighter in AD&D, you would have a large hit/damage bonus from your percentile strength (and weapon specialization). For the first couple of levels, you were the star of the show. You were the one bringing the monsters down while the theif failed to find/remove traps (or hide in shadow or anything else but 'climb walls) and the wizard shivered in his robes in the back, throwing darts. Weapon specialization (introduced in Unearthed Arcana), gave you a very potent ranged option, but it was very much a build option. If you were a bow specialist, you were a vicious archer, and still a good melee type, if you specialized in melee weapon you were brutal with, and still not bad with a bow or thrown weapons (especially with a 'strenght bow). Then there were the plethora of variants and oft-ignored rules. Every game had some extra stuff you could pull in combat. Maybe grappling, maybe called shots, maybe siezing the high ground, whatever the DM was into. The Slayer evokes some of that. His striker damage bonus makes him a bad-ass, and his stances echo a little of the plethora of non-standard options you'd often find at the AD&D table. Stances pour a little - well not gasoline, a little something mildly flamale - on the big damage fire, too. But only a little - you mostly just pick a stance and stick with (especially if you have Berserker's Charge - you lead with that, and then switch to 'Poised Asault' or 'Unfettered Fury' or whatever your other stance is until you need to charage again). Depending on your chargen decisions, you can be great at melee and not at all bad with a bow, or the reverse.
About the only AD&D feel the Slayer didn't deliver on was 2e's TWFing. Every weapon specialist and his maiden aunt used TWFing in 2e AD&D. That's why I felt the Slayer had the more 1e feel.
AD&D Fighters don't have stances or second winds, they have no power attack features, they have no feats, they have no skills, they have no separate build options based on weapons, they have no action points, they have no paragon path options, they can't push enemies, they have no reason to wear light armor, and they don't have mad charging skillz.
Well, depending on your DM you might do some mad charging, push enemies, or have a reason to wear light (or no) armor (there were some weird variants - the game was a lot less unified and consistent across campaigns than it is today), and weapon specialization certainly channeled them into weapon-specific paths. But, sure, the Slayer has feats & skills and so forth, and the AD&D fighter didn't. And, really, neither did anyone else in AD&D have feats or skills or other more recent inovations. By the same token, /everyone/ in Essentials has feats and skills and so forth. So they're not notable aspects of the Slayer. Tough, big damage, and just attacking or moving & attacking every round, that's the distinctiveness of the Slayer - and the 1e AD&D Fighter.