Having the interviewer in the room clearly creates a higher pressure situation.

Sure. But the study does not conclude that coding-challenge interviews are what tests for anxiety management. It only speaks to the effect of having the interviewer be present. But people cite this paper as though it makes an argument against coding-challenge interviews as a whole.

Is the interviewer typically in the room or no when doing a Leetcode whiteboard interview?

Typically yes.

But if a company did leetcode questions without the interviewer in the room, I find it exceedingly unlikely that people would shout "Interviewing has been saved! It now tests skill rather than anxiety!" As such, the conclusions of this paper don't seem especially relevant to the discussion about interviewing processes.

Well, it seems like either you don't understand the concept of incremental improvement, or you're being deliberately obtuse. Taking a good portion of the anxiety out of the situation can only help, right? I don't think anybody is pointing at this paper and saying "if we do this one thing, then interviewing is fixed," except people who are looking for a straw man, do you?