Anyone know how spotify may have achieved this?

There is no magic in this. 200ms is an eternity and would actually be considered rather poor performance.

Realistic latency is closer to 100ms for a cache miss (~40ms for your client to reach spotify plus another 40-60ms for their internal fetch).

You have to realize that music files are tiny and consume very little bandwidth by today's standards. All commercial music combined (roughly 30 million songs) fits into half a rack of storage.