In summary, the Op says that:
* I can't get the computer and the 2610 to communicate.
* Plus OS X won't recognise the software on the CD-Rom.
I assume that the 2610 has the maps from the disk you have already on it. If this is the case, I assume that you want to be able to plan routes on your Mac and download them to your 2610. You have, however, succesfully downloaded Garmin Basecamp to your Mac and, more importantly, you say that it recognises your 2610. However, as you say, BC only has the 'Global maps' showing, which are pretty much useless if you want to plan a route etc. But, if BC recognises that your 2610 is connected then there is a way forward: with your 2610 connected to your Mac and with your 2610 recognised by BC, look at the column down the whole lefthand side of the BC window. There are 3 main headings: My Garmin Devices, On My Computer, and Saved Routes. Look in the "My Garmin Devices" and it should show your 2610 and also what maps are on it. Click on the latest maps that are there and BC will recognise those maps and use them for any route planning. Then, when you have a route you can use BC to transfer it to the 2610.
It may be a bit of a hassle to always have your 2610 connected to your mac when you want to use Basecamp, but this will hopefully get you going.
If, however, you do not have the latest maps on your 2610 and/or want to load them from the CD to both the Mac and your 261o, then things become a little more complicated. Garmin have now standardised on Garmin Express to manage and update mapping on your computer and your navigation device. However, as has been stated the 2610 is 'old technology' and is not supported by Garmin Express. I have never downloaded mapping from a disk before, so I am sailing a bit blind here and may risk misinforming you, but I assume that there are instructions on the CD packaging. Anyway......
If GE does not work then you have to use MapInstall to downlad maps from the internet and install them on your Mac and 2610. But let's no go there until you confirm whether BC recognises the maps on your 2610 first
Good luck
p.s. it is also worth stating that it is always better (probably essential) to make sure that you are always using the latest version of any Garmin software (Express, Basecamp, MapInstall etc etc). So also look for the 'software update'/"Check for Updates" option in the pulldown menus and make sure any updates are downloaded.