The answer is one sentence, "I don't know how true this is, but it seems wise to live by it:" followed by a meme picture. The picture IS linked to the stack section of imgur, at least. At the time of this posting the answer has a positive score.
Memes are unsearchable and largely tend toward humor. I don't see SE as a humor site nor a Q&A&H site, merely Q&A.
I could see no problem with answering a question and putting a meme as part of the answer as long as that isn't the answer itself. We're told to stay away from short single-line answers in favor of more explanation and description and I think a meme is the essence of a short, single line answer.
I view a meme as a visual aid. There's nothing wrong with giving a presentation that includes a chart, but if your presentation consists of a chart and little else then you've wasted everyone's time.
Stack Exchange is for questions and answers. Not memes.
There are sites where the goal is cleverness and memelike answers -- not Stack Exchange, however.
Memes can be part of a good answer but almost overwhelmingly are not going to be able to be an answer by themselves.
Many users here are getting into the reputation where they can vote to delete answers, too, which can be useful for situations like this. As a moderator it is far easier to delete answers along these lines if there is community support (through significant downvotes and delete votes) than unilaterally doing so.
Meme or no meme, the example answer you posted doesn't answer the question, and so, cannot be considered a high quality answer.
In the general case, though, the meme answer is governed by the same rules as other answers. We expect answers to be supported by references, personal anecdotes, or the like.
A meme is no different from a short one-line answer like, "Yes, you should list a 2 week job in your resume". Someone else could post another meme with the opposite message, and the reader has no way to decide which meme to believe.
Should a meme answer ever be considered a high quality answer?
If the bulk of the answer consists of a meme, I wouldn't call it "high quality".
Of course it might get a ton of upvotes anyway - particularly if it gets on the Hot Network Questions list. Sometimes there just no figuring out the mind of the voting public.
I use pictures as visual aids on my other SE site answers such as this answer, but they don't really have a use on Workplace that I can think of. Particularly if it's just a link. More suitable as a comment I would think, and some light comedy rather than a helpful answer.
Yes, in moderation, and if it's funny. Seriously, SE is here to help people (who sometimes need humour), not just feed raw data into search engines.