I guess it's a matter of my perception. When I look at that vid I never see the front tire turn left to initiate turning right. That is also the feel I get on the bike. When I want to turn right I turn the front tire (bars) right. There are obviously other things happening at that time , Leaning, body placement, etc... but I don't conceder those under the definition of counter steering.
On my street or road race bike I am instantly aware that I turn left to go right. I see and feel it. That is what my definition of counter steering has always been.
I have read that definition before, but it is Wikipedia after all.