To a certain extent, any search engine will be "better" for avoiding some SEO tricks than Google since somewhere between most to all SEO people are only concerned with how things rank in Google, thanks to its overwhelming majority usage on the English internet - where their pages rank in the results of Bing or Yandex isn't a matter of concern to them. Granted, many of the tricks to satisfy Google are going to satisfy other engines too, but not all of them, and not in exactly the same ways or degrees. (Getting a different result page from Google and from search engine X can be a feature, not a bug.)

I personally have been using DuckDuckGo for several years at this point and am quite satisfied with their results and their commitment to privacy. You shouldn't use any Google product if you have any serious measure of concern for your privacy (he hypocritically types while a YouTube video plays in the background - hey, at least I'm not logged in).

Well, there are other search engines of course, and sometimes they're slightly better. Not great, though.

I'm really itching to start writing my own search engine now.

This is pertinent and don't think the easy answer is yes, as soon as any other search engine gets big enough the same gaming will occur.