Can anyone tell me where the money comes from that content providers are being paid?
It comes from new coins created every block, as is done with mining.
Steem runs on its own blockchain, right? Are there miners in the conventional crypto sense? If not, what is the incentive to run a node? If so, is the block reward split between the miners and the content publishers?
Yes it is all on a blockchain. It's mostly delegated proof of stake, though there is currently a small proof of work mining component (but there is a proposal out to remove PoW altogether). Yes, the block reward is split between the block producers (be they PoS or PoW) and the content reward pool. My recollection is that most of it goes to content rewards.