Do people who work at research institutes consider themselves "academics"? My long-term goal is to work at a research institute.  While discussing my career plans with different mentors, I find that there is some confusion about whether a position at a government-funded research institute is still considered "academic." Although my question is mostly semantic in nature, I imagine there are some implications with how to market myself (i.e., what to include in a CV or how to describe myself on LinkedIn).  Since many people with posts at research institutes either come from universities or go on to become professors, I think this question is relevant for this forum.
I don't have statistics, but I'd guess that if you asked the question of individuals working in such institutes it would depend on exactly how you asked the question. I would think that the quick answer would be no, but a more reflective answer, when provided with some "definition" of academic might be yes, but would depend on that definition. 

I'm also going to guess that only a small proportion of members here are from such institutes but not associated with a university. 

Of course, if a person moves from an institute to a university they would then likely self-describe as an academic. 

But if you just ask "what are you", you'd be more likely to hear "researcher" than "academic". 

But, as you say, it is mostly semantic, given that many academics do just about the same sort of thing as institute based researchers. 

The situation is complicated a bit, of course, since many such institutes are associated with universities - some very closely. It might be further complicated in situations in which industry researchers have some "training" duties, even serving as committee members for graduate students.