is it viable to ask RateMyProfessors.com to remove my entry based on
this argument when there are defamatory posting on the site?
Absent any compelling circumstances, I doubt it. By compelling I mean scenarios where a risk of serious or irreversible damage is imminent (for instance, a false accusation of rape). You might want to read the terms & conditions of RateMyProfessors, as I am unsure even of whether that website allows professors to refute the concerns raised in reviews.
The assessment you quoted about not being a public figure is inaccurate and has no bearing on defamation/privacy law. The status of private figure does not elicit a prohibition to cite the person's name in a normal website.
If a post's defamatory content relates to your profession, and is objectively verifiable as false, then many jurisdictions would --at least in theory-- recognize that you have a valid claim of defamation per se (meaning that no damages need to be proved because they are presumed). That also would occur if serious crimes are falsely imputed to you.
Additionally, if it can be proved that the defamatory falsehoods impaired your employment or career (even if in terms of demotion or inconvenient relocation), you might also have a valid claim of defamation with special damages.
If there are any defamatory falsehoods, you would have to proceed against the author(s) rather than RateMyProfessors. Since you are unlikely to know beforehand the authorship of the defamatory falsehoods, the initial complaint would be made against "defendant(s) Doe". Special care is needed in jurisdictions (such as Texas and Florida) that require the plaintiff to request a retraction prior to filing suit.
That being said, it is noteworthy that not all negative or disparaging reviews are actionable. Defamation law only relates to statements of fact, not statements of opinion. That is because, unlike opinions, only statements of fact are susceptible of being objectively verifiable as false.