Is the speech after the quotative "like" always non-literal?

In your example you are actually implying that he did say that. When you use "like" like this it's entirely possible for people to think the person actually said it, and it's entirely possible for them to think the person didn't. It's a minefield.

You could use: "He looked like he was gonna say/he was about to say ..."

Or you could just describe it otherwise like "I went to see him yesterday and he looked pissed".
But if that's too long for you, you could run the original description with the quotative "like" in your mind and see what you're implying.

If it could be taken in both ways and it doesn't do any harm if people got it wrong you can use it, it'd just count as exaggeration. And a good story's always better than the truth.

I don't think the quotative 'like' is necessarily non-literal but it might be a little strange if the quotes part is actually literal, because then I'd feel you'd be more likely to say:

"I went so see him yesterday and he said "why didn't you just do it yourself, loser?"

That would be an attempt at a true quote. 'like' is used more to report a general feeling or paraphrase. The 'quoted' part may well be verbatim, but that is not the point, despite it being labeled 'quotative'.

Given this state of things, it might be more accurate to call this a reportative 'like', but you should still call it quotative 'like' because that's how everyone else calls it.

The answers here are accurate in the fact that what is quoted after like can be verbatim, but doesn't have to be.

Honestly when I read that sentence, I kind of read it in a “Jersey Girl”, Kardashian-esque tone. That just means that whoever is speaking is either dramatizing the conversation for story purposes or repeating what was perceived to be said.