Well, the type of cutting demonstrated here is pretty self explanatory. The only thing I would suggest doing to sync your video to audio, is to use the snare as a "guide" when editing. If you want to keep the viewer's attention, you should cut on the snare or do several cuts during a break (in the beat) like they did here. Use your own judgement, however, it will be key.
For these types of videos (where syncing accurately matters), I like to use a level meter by Audiofile Engineering (Spectre) so I can have as big a level meter as I need. It helps tremendously when being this precise.
Even though there's a bit of set up involved (you will need to purchase Spectre, then download a free plug in called Soundflower to "read" it and then jump into your preferences within Spectre and chage your input). It works with vast amount of programs and you might have to link Spectre within the software you plan to use.
Like here:
Spectre comes bundled with a lot of other tools for audio too (I have no affiliation with them by the way haha).
You might also want to make sure you have a substantial amount of footage in order to avoid too much repetition. A good rule of thumb would probably be to switch "scene" every 2, 4, or 8 bars (depending on the what you feel would be the right amount per "segment"). Hope this was the information you were looking for.
-B