Have I correctly identified this part on my air compressor?
That is indeed a check valve and it prevents pressure in the tank from leaking out through the compressor when it's not running.  This is nothing specific to the model of compressor you have and you can likely find a suitable replacement for the whole thing at a dealer that sells parts for compressors.  The key thing will be get one that has the correct threads to mate up with your tank and the input hose.
Remove this one and take it with you when shopping for a replacement.