Actually it's Gyaku Tsuki, gyaku meaning reverse, tsuki meaning thrust.
Then of course there's gyaku geri or reverse kick, and my favorites, gyaku gote and gyakute nage.
Mokaido apparently means line up.
Hajime means begin. Yame or Ma-te means stop, relax, break, etc.
The basics in Karate don't translate into MMA style fighting, but Karate randori -especially if you look at Oyama's Kyokushin randori - doesn't really look like the basics taught to beginners. There's more fluidity in sparring than in the basic mechanics, but the point that Karate movements tend to be kind of rigid is well taken.
We need to remember that though Karate has its origins as a fighting method from Okinawa, Gishin Funakoshi was a school teacher who developed Karate as a means of giving kids exercise and building their character. Effectiveness in actual combat was a secondary concern. One can say the same for a great many of the traditional Asian martial arts, because they are "arts".
MMA has really brought a whole new dimension to the martial arts in that they not only condition the body and mind, but the techniques are simple, direct, powerful and can be used in certain self-defense situations. Unfortunately, one wonders how long people can last within MMA training before the injuries pile up