It's funny how people define things so tightly around themselves.
I have a friend, now the State Rally Champion, who argues that circuit racing is comparitively boring and that the fun is where the dirt, continuously changing roads and trees are.
They race against each other (via the clock) but not wheel to wheel; I contend that they are still racing.
I managed to convince a few of them (Tas' rally drivers and their cars) to my local track recently. A friend and I did camera car duty (and mixed it up a little).
I managed to broaden their view a bit and they'll be attempting to do at least one similar event a year from now on. We're still laughing about it weeks later.

I have some pretty cool video of this (three in-cars and three trackside cameras), I can post it if it's of any interest. No GT40, just my WRX again.
I know what the cut and thrust of wheel to wheel racing is like, I just decided it's not worth it for me at this time, at least not on any scale other than casual fun.
I have never been all that driven to prove myself superior to others, my drive was always to improve personally, to beat myself (I mean that in the nicest possible way

).
There are plus' and minus' to all the listed (and other) forms of Motorsport: what is "superior" to one may be boring, too expensive, too time consuming, too political etc for someone else.
People make choices. As long as they are trying to beat something tangible, whether it be the clock or someone else across a line, then in my opinion they are racing. As long as the result is not subjective then I'll continue to define it that way.
I have more difficulty including Drifting as racing because it has a subjective result. I remain open on that one.
I may go so far as to say that to my mind Hill-climb is probably the "purest" form of racing of all.
OK, just for the hell of it

:-
A dictionary defines racing as - "the sport of engaging in contests of speed".
Speed, as you know, involves time and distance. Any of the listed forms of Motorsport fit that definition in my view.
Perhaps, instead of redefining words, and telling those of us who've made different choices to call our sport something else, some of you need a new title for your pursuits, so I'll give you one :- Motor-Combat.

As Jack Brabham's (surely an adequate spokesman) view was that one should "win a race at the slowest possible speed" I contend that wheel to wheel "racing" is not racing at all as you don't actually need to be fast to win, you just need to cross the line first. A form of indoor bicycle sprint racing often has the two riders "stalled" on the track trying to gain advantage, barely moving at all. Under my new definition they also are engaged in Motor-Combat and are not in fact racing.
Long live Motorsport, including Motor-Racing and also the rather Neanderthal sport of Motor-Combat.
Tim.