First, from a cryptography point of view, transactions have to be signed, and the other nodes in the network will be able to detect and reject transactions for which the signature was forged. Second, from an incentive point of view the miner will have invested some time in solving a block that will, as a result of the previous point, not earn him anything. So we can expect he won't try in the first place.
Another way to 'award themselves with any number of bitcoins' would be to create, rather than steal, the bitcoins. Indeed, mining is also about creating some bitcoins (currently ca. 25). But if a miner was to create more than 25, the block would again, not be acknowledged by the other nodes in the network.
I think the point is that a race is not won by "adding the next block" but rather by adding a block that will be considered by the other nodes to be valid.
"However, this block means nothing if other miners do not consider the block valid. If other miners reject the block, then it doesn't matter what the block says." Okay, and how do we know that they consider it valid or invalid? Do they review the miner's work and sign a validation agreement and distribute that too or something? – Andrew – 2018-08-28T19:24:29.180
1@Andrew, another miner approves a block by mining on top if it. If they continue to mine on top of a previous block or an alternate block, then they clearly don't consider the rejected block as being the true record. – Jestin – 2018-08-29T20:55:54.397
But doesn't that require there to be transactions? Obviously it's in heavy usage today but my understanding is the blocks are pretty long. – Andrew – 2018-08-31T00:01:15.683