Arcanum has "steamworks" in the title ("Arcanum: Of Steamworks and Magick Obscura"), not steampunk. When people talk about steampunk they mostly mean the steam part of it. It's pretty much just a naming convention based on Cyberpunk (a derivative) without the substance behind it.
Every -punk subgenre after cyberpunk is a naming convention where the suffix "punk" indicates baroque technology of a period or type referred to by the preceding portion of the word: steampunk, clock[work]punk, dieselpunk, solarpunk, biopunk, and so forth. Even cyberpunk fell into this category within a few years of its existence; in the same year in which William Gibson coined the term cyberpunk, Blade Runner appeared in theaters and, although not itself cyberpunk, presented '80s noir aesthetics that were eagerly embraced by cyberpunk writers, quickly overwhelming the original punk aesthetics. The only remaining punk influences were a supposed rebelliousness and emphasis on "low life", but the former is hardly specific to cyberpunk in the broader science fiction genre, while the latter is more asserted than real in cyberpunk fiction. In particular, cyberpunk's representation in film and television tended more towards legal authority and corporate heights, starting with Blade Runner, Max Headroom, and Robocop (also in videgames with Codex favorite Deus Ex).
BioShock Infinite itself does not lean heavily into steampunk aesthetics. Columbia floats using magic quantum levitation technology, not steam power.
It's dieselpunk.
No it isn't, that's a 1940s type thing. "Weird WW2".
Dieselpunk is based on a period of technology too advanced to be steampunk but still too primitive to be nukepunk much less cyberpunk; roughly the 1900s to 1945, with automobiles and electricity, though the exact boundaries are, of course, debatab
