My reasoning is that Google has always gone after all revenue that was facilitated by something they did or provided.
I'd expect them to simply integrate patreon like functionality into youtube itself. They have most of the infrastructure for such a system in place already and could add things like patreon exclusive content.
Given Google is trying harder and harder to make money on something other than search advertising this is what I expect to happen. I expect the Youtubers will find that Google will stop them from pitching products in their video or putting affiliate links in their description. They may also start cracking down on ads that roll in the video that aren't Google placed. Then I expect them to make it a violation of their ToS to receive third party compensation for your videos, and instead to use some Google supplied version (which they will 'tax' at some rate (probably 30% given the Apple precedent)). There was already rumblings of this in September of last year : https://www.youtube.com/watch?v=TiWNSlHG-9Y
When a person clicks on an "normal link", Google notes the search terms used, the link that was clicked, the time it took you to click that link (which goes to hesitation or not), the IP address from which you clicked that link (which tells where you live), any google cookies (which if you're "logged into chrome" or your web browser can be substantial) and if you land on a web page with Google Analytics and AdSense advertisements they will know if your trip through the search engine ended up paying one of their advertisers or not.
Rather than "nothing" that is actually quite a bit of useful information that Google then resells in a variety of ways to their advertisers.
But you are absolutely correct that the person clicking the link doesn't pay any money to google.
John Doe pays $5/mo on Patreon for a youtube channel that shows how to remodel a home? He is obivously in-market for real estate, remodeling, home decor, tools, furniture, etc. That data could be worth more than $1 (a 20% cut) per month.
I guarantee you that 90% of people clicking stuff they googled are clicking on an ad (I spent $20 million on Google ads last year). This is even more true as Google provides more and more structured data on the results page without requiring a click.
This is the world we live in today, company A has some good or service that company B uses in a structural way (ie without it company B wouldn't exist). Company A decides they want/need more revenue they squeeze Company B for it, generally it eventually kills Company B.
This scenario has played out again and again, and whether it was Company B using Company A's free API, or Company A's copyrighted material, or Company A's community web site, the squeeze happens and company B usually dies.
The Dr Dobbs shutdown doesn't seem to be related to Google blocking them, just that their ad income was too low to keep it going.