It looks like you'll be seeing DOOM Eternal on the Nintendo Switch in the near future as id Software says they're "very close". The company had a livestream talking about the game, which you can watch below, in which the game's Executive Producer Marty Stratton commented on seeing a version for the Switch. Here's a transcript that's been floating around a few different websites of what he had to say.
"I wish I could give you specifics. I read all the comments, and when we say anything about DOOM Eternal, there's always the one out of every five comments is, 'Yeah, how about you tell us about the Switch?' I know people are anxious. […] We're trying to make it the best version of the game it possibly can be, so we've been working with Panic Button. They're also like everybody in work from home. It's taken a little bit longer to get there, but we want it to be everything it possibly can be. It's very close, and we're trying to be very uncompromising with what it needs to be because there's a high demand for it. We will be talking about it again in the not too distant future. It is close, but I can't say exactly how close."
It's interesting that they would use the term "close" but didn't really give any info on a possible window. Of course, some are immediately going to take that news and assume it means it will be out for the holidays. While that would be nice for Switch owners, we get why they can't bank on that being a reality. Especially during COVID-19 where we're guessing the DOOM Eternal devs are doing a lot of the work on the Switch version at home.