Sonotsugipaa

“Many” may be me editorializing, but “internet people” implies that it’s not just one person posting the same thing in many places around the web and people liking it.

If the screenshot has been shared widely enough by many different people, yes, it should be considered a meme by definition.

Then let me put it this way:

OP didn’t say that memes can’t be textual in nature, OP complains about snappy Twitter, 4Chan, Reddit (idk about this one? Reddit does have memes in some subs) or similarly sourced screenshots of texts.
Such posts, while possibly humorous, and occasionally a bit funny, are not spread rapidly by Internet users, and rarely posted with any variation.

Example 1 - this is a meme:
“Nanomachines, son!”

Example 2 - this is not a meme:

You can’t tell me what to do >:c

Vintage Story ahh meal