@critical buying a domain isnt the issue... imagine you can setup the network and open up a port so that the webcam can be accessed from outside.
Well everything works but under which IP? if you dont have a static one then the IP will change somewhen to a new one...
As far as i read, the vendor built a system so that your app will know the current IP Address. Thats it, nothing more.

Not sure how the CAM/App work but under such conditions they usually allow to configure a custom IP so you should be able to just buy a static IP from your ISP and then configure this one into the App so you dont need the vendor stuff at all, even tho i dont think that this vendor stuff is a big issue...

Cant verify this statements tho because i dont have such a cam