I understand that you want to know if you can install the SlingPlayer for Android devices application without paying multiple times.
According to the Android Market Place, you can purchase any application and install it on an unlimited number of supported devices. However, keep in mind that if you have a tablet and a Mobile phone, you will need to purchase the application for both devices, since they are different products.
The following link will provide you with further details about this specific situation:
Extending registration for SlingPlayer
Slingbox should reconsider the requirement to purchase a separate app for each device. We've owned a slingbox pro for over 4 yrs and have struggled to make it work on any device. I recently bought an Android tablet and asked if I could transfer one of my existing apps to it and was told that not only could I not do that but that I would have to buy a new slingbox pro hd and a new app. Why should I buy a new box and app when the old ones don't work?