I'd be careful how one uses the term 'jump cut'. Historically a jump cut meant a serious violation of continuity such as a cowboy holding a gun in his left hand and then in the next shot he is holding it in his right hand with no possible reason for the sudden change. Another example is when action might be moving from left to right and suddenly in the next shot everything is moving right to left, again for no reason. Errors in continuity cover a lot of area including wardrobe, make up, props including guns, where people are standing or sitting etc. In narrative film continuity is extremely important to keep what might have taken weeks to shoot appear to be happening right now.
On the other hand a jump cut where a cowboy holding a gun in one shot and it suddenly becomes a flower in the next shot would be a special case of a jump cut, called a 'magic cut'. Or another example of a magic cut is when people appear to beam up in Star Trek.
The example you have shown us uses what might be called 'jump-ahead-cutting' or 'fast forward cuts' wherein there is a reasonable amount of continuity (the background is the same, the guy hasn't changed his clothing) but to save time the editor is jumping ahead to get to the point or points. This works well with several successive discrete cuts to get rid of those awkward pauses.
Often in news interviews will use this technique and another version where instead of a cut the editor provides a 1/2 second or 1/4 second dissolve to the 'ahead' shot to smooth it over a bit.
With all due respect to AJ Henderson, I don't believe that using the term 'jump cut' is accurate because it is too general. What I think is needed here is a new term for the example sited by Jack above. Something more specific. While 'jump-ahead-cutting' is not official but only my own description it may not fit the bill.
Perhaps if we think of the original clip in the example before editing like the path of a skipping stone on a still bed of water, cutting so only the parts where the stone actually touches the water or cutting when only the stone is gliding in the air is analogous to the example. Might we call this a 'skip-cut'?