The classification system I’ve seen (including your link) puts Osteichthyes and mammals as separate classes. I haven’t seen something that puts mammals as a member of the Osteichthyes class.
Using the term “fish” in cladistics is problematic, since either pretty much everything is a fish or nothing is from a cladist point of view.
And while it’s obviously possible to name a clade that contains both mammals and “fish”, it isn’t really meaningful or pertinent to space shuttle skeletons.
Osteichthyes can be compared to Euteleostomi. In paleontology the terms are synonymous. In ichthyology the difference is that Euteleostomi presents a cladistic view which includes the terrestrial tetrapods that evolved from lobe-finned fish. Until recently, the view of most ichthyologists has been that Osteichthyes were paraphyletic and include only fishes.[4]However, since 2013 widely cited ichthyology papers have been published with phylogenetic trees that treat the Osteichthyes as a clade including tetrapods.[5][6][7][4]
Emphasis added. See also the phylogenic tree:
That is acceptable, but xkcd is making the distinction between fish and sharks, which indicates a phylogenic context.