You can write to a DVD medium if you manage to get a compressed stream fast enough. That won't be possible in software, but if you have a capture device which already delivers compressed enough video streams then it will work.
However, that is just the DVD medium. That doesn't make a DVD in the organisational sense. I am not aware of any solution which would be able to do that on a as-data-comes-in bases.
In fact it might even be impossible to start writing a complicant DVD without first having all the data, because some of the directory information (and menus etc) might require that you know precisely what will end up on the disk in the end, and this meta-information MUST be written first, hardware DVD players are too dumb to grab data off a DVD in logical order like a computer does.