This thread has spawned some really interesting thought and replies. Loving it.
To go all semantic for a moment, if you think about the word "sport" it usually implies some sort of competition. That can be competition with others or yourself, pushing yourself to previously unachieved heights of ... whatever. So if you apply the word to a car in that context you invariably end up with a car that is going to require more than the usual driving skill set to handle.
On the other hand, there are sports shirts ...
For most non-professional car owners I'd say that having a car that is fully specced for "sport" is probably impractical so it has to be a have-your-cake-and-eat-it-too sports car, which is pretty much where the Z4 falls in line (at least my old E85 does), I think. It's sporty, to be sure, but I wouldn't even think of taking it to the track, for example, because a) more dedicated, souped-up designs would eat it for lunch and b) it might get scratched.
To me the Z4 is just a "fun car" that will probably never see a day of "sport" in it's lifetime. That's fine with me, but the definition of "fun" is so broad that I have no expectations that others will agree. I want to be able to whip it around the mountain roads (without killing myself), and then I want to take it on long trips without requiring weeks of physical therapy for lower back problems afterward. I doubt that a car that was actually designed to win in a sporting situation would give me that pleasure. For the same reason I'm all for the technology that makes the car safer and easier to handle when necessary.
I'm rambling, but I guess the upshot is that I'd feel no loss if it was officially decided that the Z4 isn't a real sports car. But since cars like the Toyota 86 are ostensibly sports cars, I'm assuming the label will stick. Perhaps they should be called "sporty cars."