No, you do not need a short title on Google ( www.google.com) You might need a short title for Google Shopping (
http://www.google.com/shopping )but even this is not a definite requirement.
If you have good keywords in your listings, then you must work on building backlinks:
http://www.etsy.com/teams/11352/relevancy-and-seo-for-all-etsy-shops/discuss/9617969The keywords you use tell Google and other search engines WHAT each page of your web site or shop is about.
The backlnks are used by Google and the other search engines WHERE your listings come up in the search results, such as, page one or page 100 or somewhere in-between
Whether the search results come up with the main shop page or a listing page depends on which page using the same keywords has more or better backlinks.
For Google, use keywords in the listing title and description. Google does not see the listing tags for each listing but does read the listing description.
For Etsy use the same keywords in the listing title and tags. Etsy does not use the listing description for relevancy searches