Getting ready to upgrade from Cognos Express 10.1.1 to Cognos Express 10.2.1. Is it really necessary to uninstall the previous version?
Yes, essentially.
Port configurations are not set up to easily customize so you'll have conflicts there. The core components (TM1, BI) are not written to be deployed side-by-side on a machine (additional work there and may not be possible with other hardcodes in CX), and leaving up two CXs for any length of time would put you out of compliance for licensing.
If you use VMs, it's usually easier to stand up a new machine, install to that one, migrate content, then turn off the old machine.