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?
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.
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.
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.
This started in 2011, long before Microsoft Edge existed: http://www.chromestory.com/2011/09/google-chrome-is-now-bund...
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...
Note that until recently, Google also paid to be default on Firefox, also rumored in the one billion dollar range: http://money.cnn.com/2014/11/20/technology/firefox-mozilla-g...
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.
With IE11, which does support ActiveX, it shows ... a Chrome download checkbox. And the Google toolbar.