For ranking yes, backlinks are less and less important in Local SEO, even before hummingbird backlinks impact on local was low, but they can still be used for sending Google signals related to the keywords the content is optimized for.
Backlinks are not going away, the value of the backlinks that are not earned are being dropped. If you can easily get a link, such as the ones on directories or from blog comments, you should think twice. This is not a hummingbird change, it's a Penguin 2.1 change. Hummingbird is an entirely different algorithm where Penguin updates go after various aspects of SEO, notably devaluing links.
Backlinks are still the driving force for rankings. The types of valuable links of today are earned by quality content or purchasing old domains. I'm sure there are more methods but Google is leveling the playing field and slowing removing any types of "manipulation" techniques from the table. Internal linking will help you harness and direct any authority your site has.
If you are an expert in your field, you stand a better chance of outranking a well optimized site. SEO's aren't going away either. Just the bulls&it techniques, snake oil tactics that were used to try to game the system are being clipped.
There are lots of good reading materials on Hummingbird from the bigger brand sites. Of course, experiment and make your own assessments.
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