Domain names are an important part of SEO.
SEO stands for Search Engine Optimization.
People often forget that little fact.
Anyway, the reason domain names and URLs are important is their relation to the target keywords, and a given search engine's ability to relate the two, usually for the purpose of granting a higher ranking, or greater authority for the keyword.
When URL bars disappear, nothing will change about SEO. Humans, of course, may see your URL/domain name less, and occasionally have a harder time manually typing it in themselves. But one of the reasons URL bars are disappearing is due to the heavy reliance on social media and search engines to source clicks – for the most part, Joe and Jane Smith don't type in URLs, really, ever. They just google what they're looking for. And that's not going to change.
Long story short, don't worry about it. There are many other aspects of the changing nature of SEO, including ongoing search engine ranking algorithm changes, integration of social graphs on page authority, etc that should be causing you to pull your hair out… But the URL bar thing? Not so much.