Yes, I think that's how to be a witness.
So I can only explain it the way I understand it, if you can see it differently and it makes sense, then that's good, too. In general, you can say that "creating a new block" and "computing a cryptographic token" are the same since in the end, you get token as compensation.
However, in more detail, miner/witness are NOT token creator. The blockchain creates tokens automatically to pay miner/witness to keep the blockchain up-to-date. The energy from hardware/computer/server goes into solving transaction hash so that the entire network is aware of what is happening.
I see it like this: you and I are running a store called "SteemChain" and our job is to keep track of how many STEEM goes in and out of "SteemChain" a day. As long as we can agree on the final amount at the end of the day, the store uses that as their transaction history. The store then pays us in STEEM for our work and allocates a new amount of STEEM for the next day. All of our effort goes into keeping track of STEEM transaction. We're not actively printing new STEEM. Only the store can actually create new STEEM.