It just seems arbitrary to me to say "ok, now THIS is officially a human" when you could look at its parents and find no noticeable differences. At no point in the line of my ancestral history is there ever a hard cutoff between one generation and the next. It's a gradual progression. So how can you possibly pick a certain point in time when humans "first came around"? What criteria is used to say what exactly differentiates humans from whatever our ancestors were before 200k years ago? Did we "branch off" from something else at this point?
You're right that evolution is largely a gradual progression, but we don't have the luxury of having that gradual progression in the fossil record. We'll have a fossil from, for example, 350 KYA and another from 190 KYA. The older one is clearly not modern human and the more recent one is. So the age of modern humans is set at approximately 200 KYA, especially since genetic calculations confirm that age.
Now, if we find a 400 KYA fossil that is clearly modern human, then there'll be some 'splaining to do, but so far, nothing like that has happened.
The 200,000 years are the age of the fossils that has been classified as the first modern human. It's not like a magic number and if an older fossil is discovered the age of the modern human will be changed.
The modern human is an anatomical feat. You probably recall the look of the Neanderthals and the obvious differences between them and us, there is a whole list of anatomical feats that differ between them and us.
Somewhere between 200k and 500k years the clade Homini split up into a lot of different hominids. The others have gone extinct.