Hello My new site got sitelink in google search but instead of category its came with games link. yes this is a games site, can I change it with category here is the pic my site url is www.arcadepeer.com
I think you are not able to control how Google determines site links from your site. But I guess with the evolution of RDF, Metadata, and semantic ontology representations like OWL, it should theoretically be one day possible to indicate to the search engines an option for preferred site linking and deep site links structure to be displayed along with search engine results.
it all depends on how you setup your navigation. the way your site is now, google found easy to crawl the games links than the category links. reorganizing the site a little and adding the categories under the left menu bar to begin with might help. i see the categories on the top but for some reason googole might not think of them as categories. adding a sitemap might help. you just have too many links on the homepage which probably confused googlebot