I believe the argument is explained in the linked post by about slide 7. You simply didn't read enough. The author is not arguing that transaction volume and "work" are directly related, but rather that for the entire system to function meaningfully, mining "work" is required to secure the chain and in order for the miners to be meaningfully rewarded, a speculative market of transactions is required (the author does not agree with you that miner's are meaningfully rewarded by Bitcoins, he argues they require fiat, again see slides 1-7). So by his argument if you stopped 90% of transactions you will see a commensurate drop in mining, because the miners won't do it without reward.

This is part of a larger argument that these requirements drive the system towards centralization, thereby defeating all the work to decentralize. These are not my arguments, but they seemed to be reasonably well presented by someone who understands the mechanics of proof of work.

You're final argument that other chains may rob Bitcoin of incentives to mine may well be additional vulnerabilities of the network, I don't know.