I have some suggestions that might help you. This is a very complex and technical exercise so it is important to break it down to something that we can digest and absorb. First, I interpret the phrases not in groups of 7 but groups of 14. That seems to be where the phrases start and end to me. Thinking in 14 actually makes it easier, not more complicated than 7 because it’s an even number and you can subdivide the phrases easily. Here’s what I would do:
At least initially, forget that the exercise is in 4/4. Set your metronome to steady 8th notes with no accents. Think of it as 14/16 instead of 4/4
Subdivide the phrase. A good way to think of it is 4-4-6. Count it 1234,1234,123456, not 1-14. That makes it 14/16, or 4+4+6/16. This can be subdivided in other ways (for example 4-4-4-2) but I find 4-4-6 to be easy and effective in this case.
Memorize the first phrase and play it very slowly and steadily with alternate picking. It doesn’t appear he is dragging the pick or doing any consecutive up or down picking. Try looping the first phrase.
Start adding in the other phrases one at a time. You should start to feel comfortable with the pulse of the exercise by now.
The exercise is five 14 note phrases which then moves down in half steps chromatically from Dm to Bm. Once you have the first 5 phrases you will be able to play the whole thing.
Learning to feel this in 4/4 will take time because of the rhythmic displacement. In every bar the phrase starts an eighth note earlier starting with bar one on the 4+, then bar 2 on the 4, etc. It is very tricky. When you’re ready for that start practicing it with a drum pattern that is very obviously 4/4. This is a difficult skill to acquire so be patient.