^^^ Great first post.
The advice is very similar to what a USTA coach advises:
"When training the players the USTA works with, we usually do some sort of "running" four to five times a week. The running session usually lasts between 20 – 40 minutes, but there is a lot of variety in the types of running we do.
You’ll note that we put running in quotation marks, because much of what we do is different from the long, slow distance running many tennis players are familiar with – there is some long distance running, but the “running” sessions also involve footwork/tennis agility work, or interval runs. The type of running depends upon the periodized strength and conditioning schedule of the player.
Generally, the long distance running and longer interval repeats (400s and 800s) are done during the preparation phase when you are getting ready for the season. Shorter, higher intensity intervals (20s, 40s, 60s, 100s, 200s, and 400s) and on-court footwork/tennis agility are the main focus during the pre-competition phase in the weeks leading up to main competition or competitions. During the competition phase of the season, on-court footwork/tennis agility is the “running” focus."
Some more information on High Intensity Interval Training:
HIIT - High Intensity Interval Training http://www.intervaltraining.net/hiit.html