Depends on what you mean by the term: Some companies are in the business of supporting game studios without being game studios themselves (eg animation companies you outsource your out-of-engine cinematics to). If all your customers are game studios, you could be argued to be a 'game (support) company'.
Are the majority of Adobe's and Autodesk's customers game studios? Because that was the basis of the argument that was being made.
And just to clarify, personally, I would not describe JangaFX as a game company myself (as you pointed out, they aren't in the game business per se, but the visual effects business) - I'm just trying to clarify why the claim isn't completely outlandish.
Dunno it's just weird to say you're in the business of who you sell to instead of what you sell.
A caterer that only caters to oil camps isn't suddenly in the oil business, for example. To take an easier to understand example.
Or my brother in law runs a company that does CNC machining and sells to Airbus. He's not suddenly an aircraft manufacturer, even though his parts make it onto planes.