I was very glad to read an ELL question on screenshots and I totally agree. While reading it I tried to guess when the use of screenshots would be actually allowed, but I would really like to read a concrete guidance on this. Are we not to use screenshots at all? I did search "screenshots" in the help center index but there was nothing there.
Pictures are, in general, "inaccessible" — that is, they can't be searched for, and they can't be read by screenreader software. Someone who relies on having the internet read to them because they can't see it will be at a loss with a picture.
I would agree with the main point of the ELL answer you pointed to, but would have a little more nuance, perhaps.
Screenshots are generally unacceptable.
Where all the information in a screenshot can be presented in text, it should be. That doesn't mean that a screenshot of the original piece could not appear as well (as corroboration), but a screenshot should not be the only way that data is presented. We have a number of particularly egregious examples where a question is just a photograph of a test paper. Similarly, answers should not simply be screenshots of an online dictionary: the text should be reproduced in the answer (with a link in that case, as the screenshot actually adds nothing the link does not). Someone asking a question won't be directed to a previous similar question if the system can't find the words involved.
Screenshots are OK when they provide additional information which cannot be reproduced in text, for example an answer of mine; but even then some description is necessary to explain what that image is actually showing.
What to do about pictures:
In general, we have three options for dealing with problematic content:
Downvote. Nearly anyone can downvote any question, there is no rep cost, no justification is required, and it is anonymous. Downvoted questions are less likely to be answered, will eventually drop off the front page, may be deleted automatically, and users who post a lot of downvoted questions are automatically banned from asking any more.
Vote to close. This requires a reason, and has a minimum rep requirement. "Needs details" is often an appropriate fit for these questions, depending on how much information is present, but you could also use a custom reason.
Vote to delete. This has a higher minimum rep requirement. In most cases, this is probably unnecessary as the system automatically deletes downvoted questions without answers.
If you're feeling charitable:
If it's just a sentence or two, edit it into the question and remove the image.
If it's longer, leave a comment asking the questioner to type their question in words without using images of text. They may decide that they don't really need the entire image after all, which may make it easier to read.
If you see the same person post a lot of questions like this, or if you have other concerns not addressed here, flag it for a moderator's attention and explain the problem in detail. Moderators can reach out to problem users directly.