For undergraduate, just go wherever is cheapest with a reasonable curriculum and non-joke professors (decently difficult to hack: couple hundred citations and also real industry experience). Emphasize places that will also teach you non-CS skills (a second major, a great network that in addition implicitly teaches you the right type of communication skills, etc.).
For a masters, just don't.
For a phd, go with the best advisor you can find and finish fast.
Ignore rankings. They exist to be hacked. And academics are great hackers.
Your reference to "traditionally done in EE and ECE departments" is to say that your (and perhaps others') view of what computer science traditionally is, should take precedence over the universities' self-definitions. The former (which depends on different peoples' perspectives of what is CS) is harder to to delineate in a universally-agreeable way than the latter (which has essentially no subjectivity). So I'd imagine a website like this which is used as a wide reference, will want to reduce as much of the author's own subjectivity as possible, to actually be acceptable to a wide range of people.
That's fine as far as it goes, but the website has gotten popular as a general research ranking for a few of these subfields, beyond the original purpose of helping CS grad students choose programs to apply to. For some of those other purposes the original decisions may or may not make sense. The name of the website probably doesn't help either.
I think that excluding research in companies or universities without PhD programs is much different than excluding EE/ECE professors who happen to be at universities where the bureaucracy makes it difficult for them to have some sort of "official" appointment in the CS department. It is also much more rare that these entities publish in the top-tier conferences that csrankings counts.
Note that it is not just professors who can advise CS PhD students, it is professors who can SOLELY advise a student for a CS degree. It would help even if EE professors who have co-advised CS PhDs at the same university were allowed to be included.
I think the problem is kind of opposite of what you are saying: why should the history or bureaucracy of each university take precedence over the publication metrics when everyone seems to agree that fields like embedded systems and computer architecture are part of "computer science"?