Yes you DO need to run Captivate in Administrator Mode. But not having this set up properly doesn't usually cause the app to crash immediately on startup. If anything, it usually means you crash later on when trying to do something like capture screens. Your problem may be due to something else.
One thing that often crops up is corrupted fonts causing the crash. You can search for posts on that. Another thing you may need to also investigate is whether or not your organisation is using roaming user profiles. If they are, then that could also cause your Captivate application to crash. Captivate 6 in particular suffers from an issue where the Layouts folder that contains Captivate themes is installed by default inside the user's My Documents folder and it cannot be moved from there to another location on the user's hard drive. However, if using roaming profiles, then the shifting location of this Layouts folder has been known to cause crashing.
I have discovered why Captivate 7 requires Administrator mode. (at least partly)
When is starts and when it is running, it creates a random file in C:\ starting with the word "photoshop".
User accounts (and user software) do not have rights to write to the folder, and for good reason.
You can free up the rights for C:\ for users, in two steps: Reduce the integrity level to low, and grant "modify" rights to users. This is not ideal, but better than making it run in Administrator mode.
There may be other features which require Administrator mode, but is not clear why this should the case.
It would be better that this was not required, and I hope Adobe fix this when it is next updated.
Captivate also requires Run As Administrator access so that it can perform screen captures and access the system audio to record during capture sessions. So there are actually several reasons why it requires this deeper level of privileges.
I'm having issues with Captivate 6 files not publishing properly and I don't have admin rights on my computer. I right click and open Captivate with admin rights but when I publish I can't get the htm file to play. I have reviewed the setting compared to Capt 5.5 and they all seem to be set properly but the file still won't play.