What software can I use to make "stop motion" video from existing video material
You can use any non-linear video editor to make this, but you are in for a lot of manual work.

Time posterizing (or video strobe) is mentioned which can give you that "stop" effect, but it will not take care of the walk-cycle. For that you need to manually go in and choose each frame.

My suggestion would be to take the video sequences you need, go through frame by frame in the preview monitor and grab the frame you need according to where in the cycle by making the in and out point the same, then drag the cut (a single frame) onto the timeline. Repeat.

Now the only thing you need to do is to scale the timeline so that each image has a duration longer than 1 frame (probably around 10 frames or so). With this technique you can also fine-adjust a single "take" if needed.

The other approach is to convert video (or using photo still) as single images. Here you loose the advantage of fine-adjusting though (in relation to the walk-cycle).

Automatically detecting where in a walk-cycle a person is is highly specific task and AFAIK there exist no such software available to the public (some law enforcement agencies have access to software for behavioral analysis including walk patterns, but that becomes quite a different table- - so yes, it's possible, but not available).