Rich Internet applications (RIA) are web applications that have the features and functionality of traditional desktop applications. RIAs typically transfer the processing necessary for the user interface to the web client but keep the bulk of the data (i.e., maintaining the state of the program, the data, etc.) back on the application server.
Current desktop applications need compute power and so RIA will need more processing power for richer user experience. So these can take advantage of multicore processors to do things quickly thus enancing UE even more. Also, the second sentense says that it tries to tx processing power to the client. Particularly if you have multiple apps running in your desktop with RIA then you are going to see significant delays as all these fight for a CPU resource while in muticore it is not the case.