Hi, I don't think that's right, sorry. It refers to the user's own account(s) in various MediaWiki projects. See w:Special:ListGroupRights for an example usage of that message. This page is a list of rights that users can have. As you can see, one of those rights is the right to merge their account in the various MediaWiki projects into one unified account. See meta:Help:Unified login for background information on this system.
In this message, "their" is a case of the "singular they", so it should be translated as "merge his/her account". In Interlingua I translated as "fusionar su conto" but perhaps "fusionar le proprie contos" would be better.
You're welcome. I decided to follow you in that translation. Not that it matters much, as there are probably not many un-merged accounts left in the MediaWiki projects now...
It's nice to hear that you use Interlingua as an assistant language. It's similar to Galician and many other languages. The funny part is that those other languages are not as similar to Interlingua. :)