I have been having problems with this issue as well and also running as admin doesn't work.
Critical Error
53 - File not found
Critical error while checking for updates. Update process aborted, if this continues please let us know on the forums. ...
when i press OK button it brings me to profiles and launches properly but when i get in and press play RS it wont detect my game installed or wont detect it even when i re download the game. it just brings me to the RuneScape main page with the try free and download button. or pops up with a small window telling me to download the client or disable the client but when I click download it opens google with a 404 page not found.