It appears that video support for Opera 9.20 (I think all the 9.x versions too) doesn't work correctly with default gentoo's netscape-flash (versions 7.x and 9.x).
There is a simple solution for this problem which needs to modify netcape-flash ebuild (or opera ebuild?).
Here are some URLs on this problem:
In short, the soultion is to:
1. Make a symlink from /opt/opera/lib/opera/plugins/libflashplayer.so to /opt/netscape/plugins/libflashplayer.so
2. Show a notice after merging netscape-flash about need to edit ~/.opera/pluginpath.ini file and set /opt/netscape/plugins=2 . Opera should not be running when performing this.
After this changes Youtube videos work great (just as any (?) other Flash videos).
I think netscape-flash/opera maintainers will find the best way to acheive the desired effect.
*** This bug has been marked as a duplicate of bug 127200 ***