Hello Richard,
have a look at rtl_tcp.
You would need users to run rtl_tcp and then you should be able to get the data from the network with your own proprietary software.
I have no experience with rtl_tcp, but it it would not do precisely what you want you can modify it and make your modified version available with an opensource license.
As I understand things: Once the data is on your local network it has left the world of open source and you should be free to process it whatever way you want.
Regards
Leif
If I write software that uses the rtlsdr library that is already installed on the computer, does my software also have to be opensource?
Thanks, Richard