Is there some maximum length of a movie clip that can be publicly shared as "fair use?"
E.g., the Youtube channel Movieclips shows clips with an average length of 2:30.
NOTE: This answer assumes jurisdiction in the US.
No. Length does not determine whether or not something is fair use or not. There was a court case (Harper & Row v Nation Enterprises, 471 U.S. 539 (1985), all credit to Dawn) where it was determined that just a few paragraphs from a 300+ page biography were infringing content, due to them capturing the "heart of the work".
As user6726 said, in your example the clips you mentioned are most likely licensed.
Also, courts tend to look poorly on things that are simply "shared" claiming fair use against copyright claims. Now, if you were to use a short clip as an example of something you were explaining, teaching, or critiquing, that would be different and would more likely be fair use.
It is important to note that there is (by design) not a clear cut line if something is or is not fair use. There is a set of guidelines, but determination is made on a case by case basis There are a couple of cases that it is out and out NOT fair use, but none for fair use. This is because fair use is an affirmative defense, which is to say, you admit to the offense, but claim an exception to the rule. Self-defense as a defense to charges of homocide, assault, etc. works in a similar manner.