"Why am I being asked to update Appel Remote Desktop . . ."
It's part of the operating system - always has been since at least 10.2 (Jaguar). You should update it whenever there's an update available.
". . . when I don't have or want Apple Remote Desktop?"
You do have it and it's called Remote Management. You'll find it in the Sharing Preferences Pane. Whether you want it or not is entirely up to you. It's not on by default and is in no way a security risk, a virus, an exploit, malware or anything else that may be seen as 'nasty'.
Read this for more information:
Page 3 basically says it all. On every mac OS there will always be the client version of ARD. The manual mentioned above is for the administration part of ARD.
If this is the only computer you have then you will probably never ever need it or use it. But that does not mean you should not update it when the update for it is available.