Besides the power output and the name, what is so special about the Alpina?
Not as much as there used to be. Alpina's of the past evolved from tuning packages for BMW's, to be much more complete products, with their own personality and traits. What then kicked it up a level, for me, was that they'd go about things in a very different way, delivering something like the B8 4.6 or the B10 Bi-Turbo as a complete package. The B8 was unique in being a V8 powered E36, the Bi-Turbo unique in being the Turbocharged alternative to an M5 when M cars were strictly naturally aspirated. Then there was the B6S, which was an inline 6 M3 before M3's had inline 6's. Sure, lots of tuners would sell you bits and pieces or do the work, but not presented as a finished item, with its own unique styling, interior trim, suspension upgrades etc.
Things started to get a bit tamer on the engine front, but they still did interesting things that BMW weren't doing. In the absence of things like M3 or M5 tourers, or a high performance "M7", Alpina would have an offering.
Nowadays Alpina don't really offer anything truly unique, with the products mostly being analogous to M-Performance products. Which is a shame. Although Alpina is its own company, the products mostly roll of a BMW production line... it's still a great opportunity to offer a product that BMW can't justify the business case for.... but that's not how they're using it. It's treated largely as a trim level now.
Cars like the rumoured Alpina i8 would have been ideal to inject a little bit of differentiation into the brand, but still, I'd like to see them going back to making more unique things... perhaps even going a step further and entirely rebodying a car as an Alpina only model, along the lines of the AMG GT-4 Door.