DDG is not a browser, it is a search engine -- that article is not talking about search engines. Search engines are just websites, they cannot make any difference with the other websites (i.e. gmail) you use. That is also definitely not the HTML version of gmail you're seeing -- it's not crazy broken like you've experienced, just less blingy.
I will say, it's quite strange that the issue only occurs when you use DDG, but I also don't fully understand what you mean there. When you go to GMail, what web browser (Firefox, Safari, Chrome, Internet Explorer, etc.) do you use? Are you switching to Google Chrome
when you say "tried opening my GMail with Google itself," or are you searching for "gmail" on Google rather than on DDG?
In the former case, what web browser are you switching from
In the latter case, does it work when you click a direct link such as this: https://mail.google.com
I don't actually see how the latter case could happen, but interested to investigate this further.