You might (but probably won't) have guessed from the title that this game stars the 80s-90s metal band Seikima II. I hadn't actually heard of them before playing the game either, so don't feel too ashamed. As it turns out, they're pretty good. A bit of backstory that's (sort of) relevant to the game: the band is a group of high ranking demons sent to earth by Satan to spread his worship and also to conquer the earth through the medium of heavy metal. This is relevant to the game, as the game's villain is Zeus, king of the gods and enemy of Satan, who has kidnapped four of the band members of Seikima II, leaving only the singer, Demon Kogure to save them.
He saves them by jumping around various locations collecting stuff. Stuff like heads, ku klux klan dolls, apples and so on. The basic idea of the game reminds me of old british computer games, like Bruce Lee and Jet Set Willy, in which the goal was to explore large maps and collect all of a certain kind of item. This game doesn't have one large map, though; each missing band member is trapped in a different stage, and each stage is split into eight areas, each a few screens wide. As well as the items needed to complete the stages, there's also health increasing blood potions and money. The money is used in the shops (represented by big eyeballs) to buy extra blood potions (which should only be done in emergencies, dues to the scarcity of money), weapon upgrades and musical instruments (one per stage, they have no in-game use, but are necessary to get the best ending).
The "special" part of the game's title alludes to the fact that it's an upgraded port of a Famicom game, the most obvious changes being improved graphics and different jump physics. In the original version, there were two kinds of jump available: high jumps, done by pressing the jump button then left or right, and long jumps, done by pressing jump and left or right together. That system felt stiff and strange, and the more traditional jumping that replaces it in "special" is much preferred. Pointless semi-related trivia: I first heard of this game when I saw Arino buy a copy of the Famicom version in an episode of Game Center CX.
In conclusion, this is a pretty good game. It's nothing special (aaaahhh!), but it is definitely an improvement over the Famicom original. Plus, Seikima II are cool, so that's a bonus.