On that alone, I am very doubtful on that article.
This is also distinguished from what I have taken to calling a "pre-flight checklist" at the start of large programs, making sure databases are connected, requisite tables are present with the correct columns and datatypes, that specific files or directories exist, that files may be of a certain "freshness," and so on.
I'll stand by it: sanity test is a lot more descriptive and useful than "quick test." Those footnotes are only kicking the can down the road of justifiability. But let's examine them according to the aforementioned The PC Replacement is Less Useful criterion.
Recommending just "test" is ... well, double-plus ungood, in the sense that we now have no idea of the qualities of this test and how it could be distinguished from some other test. Hard pass.
"Confidence test" only implies a statistical likeliness, like a confidence interval. It does not imply the This Ought Not to Happen of a sanity test.
"Coherence test" is interesting but ... coherent against what?
If someone wants to sell me on a replacement, they are free to try, but the replacement must be at least as good at communicating what it does as the term sanity test. If this fails, then it will be scoffed at, and should be.