Currently, the only way to get Killer Instinct Classic is by purchasing either the Ultra ($39.99) or Ultimate ($59.99) edition of Double Helix's new Killer Instinct. I say "currently" because these things have a habit of getting out there as standalone releases but, for now, producer Torin Retting has confirmed to Siliconera that Classic is tied to the aforementioned editions.
"It includes the original arcade ROM (v1.4) with all of the classic, fan-favorite glitches, and the revised version (v1.5D) that came out later to fix things like Cinder’s infinite combo. In addition to this we’ve added cool extras like a training mode, frame effects like scan lines to emulate a CRT and galleries of the original sprites."
The other bummer here is that Classic doesn't support online multiplayer, at least not yet. Retting says the team has been "talking about it a lot." Go ahead and add netcode, then put the game out on Xbox Live for a reasonable price -- that'd be just lovely, Double Helix.