I read on the Wiibrew site that DVDX has been replaced by the Homebrew Channel itself. However, all I can find through many searches is using MPlayer, which isn't "the Homebrew Channel itself." Either Wiibrew lied, or I'm missing something.
You still needed to use something like mplayer or WiiMC when dvdx was around. It just worked in the background to allow those apps to play DVDs. Now hbc does that background job itself, making DVDs accessible to homebrew apps. You still need to use something like mplayer or, even better, WiiMC to actually play DVDs, hbc just enables the access for those and other apps
The Wii is compatible with GC games. Unless you got a new Wii without the GC compatibility, in which case DVDs won't work via homebrew anyway, due to hardware changes stopping them working (this is also true of any older Wii with GC compatibility made recently).