Amen to every comment about this.
The minute-by-minute gameplay of Splatterhouse 1/2 and 3 is nothing to write home about. As a one plane beat 'em up in 1/2 it's a bit slow, clunky, and jank. As a normal beat 'em up in 3 it's equally as clunky and on par with other B tier console fair like the LJN Spiderman games or Growl/Runark.
Atmosphere was what it had though. Part 2's intro and first level perfectly set the tone: your girlfriend is dead and your only hope is a demon mask that you shouldn't trust at all. I will gladly concede that gore =/= horror, but Splatterhouse 3 delivered some genuinely disturbing moments. The possessed teddy bear with mutant arms, the dick worm on legs that laughs like a little girl and whose head turns into a pile of maggots while it still writhes across the floor to attack you... that's about as scary (not just gross) as contemporary 2D spritework got.
The cinemas, limited as they were, still conveyed a sense or urgency and dread. You wanted to hurry through levels because you didn't want your wife to be eaten by boreworms or your kid murdered by monsters. You genuinely cared about the characters and the outcome.
At the very least the entire trilogy played everything straight. Sure, you're in a shed murdering demon fetuses with a chainsaw, but there wasn't any wink wink nudge nudge 4th wall goofiness going on.
The remake was a joke. I knew before I even played it when I was reading these long winded interviews from the developers talking about such admiration they had for the source material. This was followed up with tennis shoes, jorts, and goofy ass character models, and lots of flagellation about gory kills and what they had to add to the mythos.