Yes, a 2008 iMac is too old for the Internet recovery. Oldest for that feature are 2010 models.
(note: your 2008 iMac would have originally had OS X 10.5.x (Leopard), about 4 years before Mountain Lion was released
)
If you have purchased Mountain Lion, it will show up in your App Store, Purchases tab. You can download it again, assuming that the Mac can boot to Mountain Lion. If you are running Yosemite, App Store will warn you that you can't run the Mountain Lion installer, which is true - but you can still download it. Once the download finishes, you will have the Mountain Lion Installer app in your Applications folder. Next step is to create a bootable USB flash drive from that app. You will need an 8GB flash drive for that. You can follow steps to create the bootable installer, or just download DiskmakerX, which makes the process simple.
And, you will have a permanent copy of the ML installer that you can use again, without waiting for the long download…
Or, another option is to actually purchase
the Mountain Lion installer from Apple.