Generally, yes. Most of the Bibles on Bible Gateway fall under a publisher's copyright. Most publishers allow for some limited personal use and quotation, but you will need to check each version's specific copyright information before using them outside Bible Gateway. Versions in the public domain can be quoted and used without restriction.
You can find out more about a Bible's copyright status, and view its re-use policy, by clicking on its name in this list: http://www.biblegateway.com/versions/. Click on a Bible version name in that list will bring you to that Bible's Version Information page, which contains relevant copyright and ownership information about that Bible.