^I've always taken "regular" to mean someone who appears in, or at least is credited in the main cast list of, every episode. The supporting TOS players were never more than semi-regulars. Even Kelley was missing from two first-season episodes. Nichols was in 65 episodes, Doohan in 64, but Takei in only 51 episodes and Koenig in only 35.
This is pretty much my take on it too.
In season one Shatner and Nimoy were the only 'regulars', the rest of them were recurring players. Season two seen Kelley being added to the list of regulars alongside Shatner and Nimoy. I don't know the ins and outs of Doohan and Takei's contracts. I imagine they were on some kind of a retainer -- but, episodes certainly weren't obliged
to use them like they were the "big three" stars. I think out of the entire second tier cast, Doohan was probably in the strongest position, as his character seemed to strike a chord with people, and the production team found themselves wanting to make more use of him. Nichols was indisputably in the weakest position. Not a slight on either the character or the actress, but she was only being employed as a day player and whether she appeared or not was entirely at the discretion of the producers.
Some confusion set in for the proposed 1970s 'Phase II' series and TMP. I think the assumption was made in the 'Phase II' bible of many of these secondary characters having a greater importance to plots (there was some doubt as to whether Shatner would even remain with the series beyond its first 13 episodes, and Nimoy was of course gone completely). As the movies progressed, the status quo of Shatner-Nimoy-Kelley reasserted itself, though the supporting characters had kind of finally become indispensible by that point.