LOL... no Joe, the first horse is not pacing.
A pace is where the front and hind leg on the same side hit the ground at the same time (a 2 beat gait.) If you go over to YT, it might show up more clearly (it does for me) and watch the front and hind hoof on the camera side, you will see the rear hoof hit the pavement well before the front hoof does.
This horse is doing the signature gait (single-footing or 4-beat) of the RMH, KMH, and MPH....and they do not bob their heads. My horse does not bob his head either (but my old TWH had such a big head nod during his running walk he would bob his bottom lip.)
This gait is not like the running walk, the Foxtrot, or the tolt.
Although hard to hear in those videos, the sound of the hoof falls is also a clue. The different gaits of gaited horses make different rhythms.
Try here- http://www.brightonridge.com/about_gaits.html
The top horse in the video on this chart is pacing. The rest is a quick primer on the more common gaits.
If you re-watch the horse in the first YT video I posted above.... note how the tail bobs up and down. When a horse does a pace or stepping pace the tail doesn't bob up and down like this horse, but rather slightly side to side (with just a little bobbing up and down) and it creates a different tail movement.
I don't have the links anymore, but there are some really good sites out there where they film the horses wearing different colored tape or boots on the legs which helps the viewer follow the gaits to get a better understanding, along with using horses with shoes on hard surfaces so as to hear the distinct rhythms.
There is also articles on the tail bob and waves with videos.
Try this one-
Although not perfect, this video has the clear 22.214.171.124 footfall pattern (as opposed to the 1.2...3.4 stepping pace or the 1..2 pace) and the horse has a white front hoof marking making it easy to follow it and see he is not pacing.