Your horse does have gait.
Here is what I see:
Flat Walk: Your horse flat walks, at the walk she is a bit lazy and goes in and out a bit because she is strung out and doesn't want/know how to engage her back end. By pausing it you can see her back leg swing under and the leg in front of it lift up to get out of the way...that's walk....but with her being strung out, it is easy for her to not use her rear and step pace. Walking horses get a lot of their blance from their back end when they are actually walking and so if they are not muscled, or do not have their balance at speed they will go out of gait and do what they have balance in at speed. The step pace is really smooth and if you're not looking to show or have a perfectly gaited horse, it is nice to ride...my mare did this when I started her training, but now that she has her muscling and blance she essentially stays in gait all the time, it just takes some time to get them there.
Either way, she's beautiful, love her markings! She has a nice back end