Sincere question- assuming that '7 minute workout' is an HIIT - what kind of warm up does something like that require and how long? I want to do the 7 minute workout but I'm worried it needs a warm up.
Initially go light at 7m workout, that would serve you as a warm up. Once you are able to push, add one more session right after (maybe 5 minute break in-between). Your first session stays warm up session. Once 2nd session is not enough (in like 3-4 months), add a third one. Then you can increase intensity of all exercises a bit (still keep the first session lighter). In 1 year you'll be in best shape of your life (given proper food & sleep). Good luck! ;-)
Another way to do HIIT is to grab a stationary bike and do intervals there, e.g. 3 minute warmup at low level then increase difficulty or start pedaling faster for a minute. At some point you'd start reducing breaks in between, maybe in 1-2 years you'd do at most 10s low-intensity in-between.
The short description of the study in the link indicates 4x4 minute intervals at 85-95 percent with rest between sets which seems more like VO2Max intervals than HIIT and is described as High Intensity Interval Exercise, your description is closer to ballpark what I know of as HIIT, sometimes called Tabata intervals, which definitely need a warmup that depends upon you but 20-30 minutes is the minimum I strive for.
7-minute workout is mostly a myth. You can do a very intense and thorough workout using the 7-minute routine but all the reported benefits involve working yourself up to 3 repetitions of the 7-minute routine so it really takes 21 minutes.
Some of the research showed significant health improvements from 3 days a week of 3 reps of 20 second standing bike sprints. So only 3 minutes per week.