Umm, yes? Kinda by definition. If you state that you will not, under any circumstances, do something, you are, in fact, delivering an ultimatum.
Under that definition, pretty much everyone is routinely delivering ultimatums, just establishing basic things like game system, time and location, drug use (including alcohol) at the table, what sort of sexual themes, time, and a bunch of other things. Most people are going to have a hard line on at least one of those - it's a rare person who's fine with literally any time/location since most people have jobs and aren't going to take a plane flight for a session, or who's fine with anything from 'never even mention kissing' to 'explicit ERP including visual aids', or fine with anything from 'no one may drink any alcohol at all' to 'we're going to pass out drunk every session and maybe throw in some harder drugs too'.
If everyone is constantly issuing dozens or more of ultimatums as a matter of routine, then why even point out that someone is issuing an ultimatum? What's the significance of 'issuing an ultimatum' if it's just a routine thing literally everyone does? In the original message I responded to, the DM 'issuing an ultimatum' was intended to paint them as doing something bad and out of the ordinary, but it's a criticism along the lines of 'the DM was breathing' - everyone at the table is breathing unless you manage to get actual undead to show up, pointing it out doesn't have any significance.
I don't think it's a problem if they don't want to GM. It does become a problem if they're using their position to force a particular game or play style on the rest of the group.
If a member of my play group said "It's my house we play at, so we're going to play 5e because it's my house" with actual sincerity, then I'm going to leave the group. That's not how friends treat each other, and I have no interest in playing with people who aren't friends (or at the very least friend-adjacent).
These threads are always so bizarre to me. The idea of demanding that someone host a game at their house that they don't want to participate in and accuse them of being a 'bad friend' for their gaming preferences and limits on who they allow into their own space is absolutely foreign to me. I respect my friends' choices of what hobbies they like and don't like (some don't play any RPGs at all!) and on what they want to allow or not allow in their own homes, and I think that the blatant disrespect of treating someone deciding what games to participate in and what activities to host at their house is the 'not how friends treat each other' behavior. But it's so outside of my experience that if someone did react like that, I'd assume there was some deeper grudge than 'Dave doesn't want to play X game, and if we're running a game Dave doesn't want to play he's not going to host it'
A: I am going to run Game X
B: I'm not interested in playing Game X, so, I'll bow out.
A: But, we game at your house... if you bow out then none of us can play.
B: Well, according to the collected wisdom at En World, I should never have to compromise, so, I don't want to play Game X. If you're running Game X, I'm not interested in playing.
A: Well... I guess we're going to play Game Y then.
Why doesn't A offer to host, or find another player to host, or find another location to play in, or play online? I've played games in dorm rooms, in apartments, in off-hours classrooms, in parks, in gaming stores, in people's basements, in people's garages, and a lot of places over time, B's gaming room is not the only place in the world where it's possible to game. This sounds like B trying to guilt-trip A into doing something A won't enjoy because it's easier than B sorting things out, and again I'd say that's the 'not how friends treat each other' behavior. Though again this is one of those 'don't see it IRL' things because I just don't know any As who'd demand B host a game B doesn't want to play.