The question is, is a class classified by what does the most damage in their kit?
Or by the style of gameplay that playing it involves?

Again, speaking from a summoner's perspective.
I spend maybe 1 second every 30 or so seconds having a short thought to keep up the dots (at most).
Most of the time I'm busy with which of the many OGCD skills I have to press next, which bahamut/phoenix phase is up or up next, which ruin to use etc.