They still do it: https://get.adobe.com/reader/ (Checked today, Windows 10, while using Edge. Default checked on this page is to also install Chrome.)
It's worth noting that Sundar Pichai's claim to fame at Google, prior to Chrome itself, was getting the Google Toolbar installed on everyone's PCs whether they wanted it or not. The CEO of Google isn't just a fan of software installation dark patterns like this, he's the guy responsible for it at Google.
Because Edge doesn't support the Adobe Reader plugin, and to avoid a support nightmare Adobe seems to recommend downloading a browser it does work with.
I visit that same link using Firefox on Linux and don't get a Chrome install checkbox on the page, but maybe someone else is?
Adobe Flash is directly built into Microsoft Edge, they collaborate on this. Chrome doesn't support ActiveX or NPAPI plugins either, and the Flash plugin also doesn't work with Chrome, because similarly to Edge, the Flash plugin is built directly into Chrome.
Also, Adobe Reader is a standalone program, you don't install it to embed in the browser. (Both Edge and Chrome can display PDF files natively.)
This has nothing to do with "recommended" apps. Chrome is pushed with Adobe Reader because Google pays them to do so. Similarly, McAfee pays to have their software installed with the Adobe Flash plugin installer.
Adobe Reader plugin doesn't work with Edge, because Edge doesn't support ActiveX. The Adobe Reader installer also installs the browser plugin.
You linked to the Adobe Reader download page, which asks you to install chrome if you don't have a supported browser. Which you didn't.
I get that you have an axe to grind here, but it seems like you're cherry picking an example of where Edge doesn't support something so Adobe is recommending a supported download.
Adobe doesn't recommend the Chrome download when visiting with Firefox, for example.
Note that IE does support ActiveX, but Reader still not only tries to bundle Google Chrome, but the Google Toolbar as well.
You're creating an incredible work of fiction to avoid a long-standing well-known truth: That Google pays Adobe to bundle Chrome in their installer when the user is coming from a Microsoft browser. (If I come from Firefox, it offers McAfee's Security Scan Plus, which also pays Adobe for the privilege.) This isn't a technical or compatibility issue, and it never has been. This is where Adobe makes money on Adobe Reader downloads.
We don't know the dollar amount of the deal, as Google keeps those sorts of things confidential. But it is very similar to the figure an Oracle lawyer dropped, that Google paid Apple a billion dollars to keep Google as the iPhone's default search: https://www.bloomberg.com/news/articles/2016-01-22/google-pa...
Some additional reading on this strategy, is that Chrome came about as a fear that Microsoft might disable or cripple the Google Toolbar, which was used to push people over to Google Search and collect their browsing data. (And was also heavily promoted as a bundle item in other installers like Java.) Sundar Pichai, now Google's CEO, spearheaded the toolbar and then Chrome: http://fortune.com/2014/10/27/google-rise-of-sundar-pichai/
If you believe Google got where it was by being "the best", it may be hard to realize this, or easy to overlook the facts. But Google's market share is largely a result of paying for other companies to push their products, with or without user permission.
The Chrome distribution deal with Adobe was always Windows-only, as far as I know. So I'm not surprised you're not seeing it on Linux. That said, Adobe is just showing whatever they were paid to show, for whoever the target audience is. With Firefox on Windows as of today it shows checkboxes for some antivirus programs instead of Chrome; I assume McAffee outbid Google here.
With IE11, which does support ActiveX, it shows ... a Chrome download checkbox. And the Google toolbar.
But in terms of the ethical question, we're now talking about how if I break into your house to steal all your unhealthy potato chips that's better than if I break into your house to steal your money. The fundamental problem is breaking into your house.
It's worth noting that Sundar Pichai's claim to fame at Google, prior to Chrome itself, was getting the Google Toolbar installed on everyone's PCs whether they wanted it or not. The CEO of Google isn't just a fan of software installation dark patterns like this, he's the guy responsible for it at Google.