A "datacenter" to me, is anyone who has direct access to their servers, whether they be in a cage or a locked rack that belongs to them. They have their own IPs, they're responsible for the network to some varying degree and they sell dedicated servers or colocation services.
What is the breakdown of a datacenter when it goes to an end user?
Building owner, large company.
--> Another company rents out a suite or an entire floor or large area.
----> That company sells a cage with 4 racks (example) to another company.
------> That company then sells dedicated servers and can provide limited colocation.
----------> Colo client of the above sells you servers.
etc
Thats about as far down the chain as I'd go to consider anyone a datacenter, personally. My example isn't very good as there could be a lot of various middlemen and you can always point out areas of the infrastructure that is out of the control of some, etc. But having a small cage or a rack, to me, is to being a datacenter as being a hosting-reseller is a webhost. Both are technically true, and come with their own set of responsibility that make it true, but barely meet the requirements to make it that way. (I think, anyway. That's just me)