That is incorrect. The validity of a transaction depends only on how it relates to the transactions that precede it. Mining simply keeps track of the "official" history of transactions, to guard against double-spend attacks.
Transactions are useless unless they're confirmed in the blockchain. That's the whole point of bitcoin. Mining and the blockchain is all there is to bitcoin.
And that's another problem: the energy used for mining depends on the hashrate, not transaction rate. It's true that increasing popularity of Bitcoin rises both, but trying to calculate "energy per transaction" on that basis is pretty much the same as trying to calculate "drowned people per litre of ice cream consumed" on the basis that warm weather increases both.
You might have noticed that my calculation started off with network hash rate because that's where the energy is being used. I don't really think it's that important a calculation anyway, but I did it to show the $35 per transaction of the OP was incorrect. Indeed, if the transaction rate goes up faster than the hash rate, then the transaction cost is even lower.
Instead of criticizing, maybe you can come up with a better cost per transaction for bitcoin (because there surely is one).