Such a solution would be just for this unknown dlna/upnp device. There is no single solution to solve this. When posting please include make and models as well as the OSes in play.
And even then, this may have you debugging the setup. For example streaming to the PC over WiFi ate up a lot of the WiFi bandwidth so to re-send that to DLNA may result is less than stellar play.
After all that, why not some sub 35 buck Amazon Fire TV stick? It does YouTube just fine.
Is there software like Tubio for Android that can stream youtube to TV or media device with enabled dlna/ upnp.