HITs pretty popular, I've seen alot of articles over the years on this, videos, etc. Fairly easy-going exercises in that video, though done in that sort've circuit style manner - it can really test you, especially if you lower the rest intervals.
Bodyweight exercises [like in that video] are what I've come to focus on more over the years, instead of freeweights, did freeweights for a number of years, and while I never suffered any serious injury doing compound lifts, I knew that overtime the possibility of me putting unneeded stress on my joints would grow greater, even when done with good form/execution, there's always that slight 'tweak' that can sometimes happen that you might not feel til days later [lower back, rotator cuff6, etc].
What's great about continually doing bodyweight exercises, especially when after time you start to variate by changing angles on the exercises slightly, you can/will gain a body composition and type of strength/athleticism that's only gained through continually working with bodyweight exercises, something that weights won't provide. Don't get me wrong, freeweights can be used to build functional strength, though they have to be worked with in a different manner [not in the traditional sense]. [This is coming from someone that stucks with freeweights for a number of years].
Kettlebells have became popular over the years, they're an unmatched form of exercises in terms of muscular endurance, lean muscle production, and biggest of all - functional strength. With kettlebells there's a huge emphasis on 'swinging style' exercises, exercises that start from the legs/hips, and travel up the back to the middle/upper back, then arms, shoulders, so on and so forth, essentially a full-body workout. Also grip strength tends to improve greatly over time. I have a 26lb, a 15lb, two 40lb and two 65lb KBs. About 60% of my workout consists of using these. KB's have became extremely popular in submission grappling/brazilian jiu jitsu over the years, they seem to directly translate over for me - all the heavy unorthodox swinging motions coupled with the strong grips, continual cardiac output, muscular endurance, these things play heavily over into the grappling world. Also, KBs aren't as boring also, compared to just sticking with freeweights, KBs can actually be incorporated into that beginner HIT video you linked above.
25 minutes at 2-3 times per day definitely isn't overdoing it, especially with those specific types of exercises, great beginner program you got there.
I always change things up, change angles on exercises, rest intervals, time under tension alterations, always try to keep the body adapting, because after awhile of doing the same exercise/s over and over, week after week - the body gets used to and adapts to suit the needs of these situations, so being creative for me is important.
I recently picked up a 50ft shipyard rope [called 'battle ropes' by the people that sell them], has two handles on the end, sling one end around a pole or some similar object, and bring both handles even to you. From there there's a variety of exercises, mostly done in a fast, tempo type format, essentially making continual 'waves' with the ropes, making sure that when you begin the waves that they make it all the way down the whole length of the rope to the end. Most of the exercises I will do are in 30 second intervals, with a 30 second rest in between. Using this rope is a brutally effective way of building up your lactic acid threshhold, intense muscular endurance, and hugely - cardiac output. I'll usually do a 20-30 second burst with the rope, rest 30 seconds, repeat for 3-4 sets, rest one minute, then go on to the next exercise with the rope. There's about a half dozen exercises I do with mine.
Typical routine for me is 30-40 minutes with the kettlebells, maybe throw in 1 or 2 compound lifts with freeweights [usually squat, romainian deadlift, or a barbell clean n' press]. Don't mess with bench press any longer, as I started having slight rotator cuff issues off and on, and knowing that it surely came from that - I ended up cutting that specific exercise out. The last bit of my routine I typically will always end up doing several variations on chin ups, kip ups, and pull ups on a bar that I have fastened from two 2-inch chains, which in turn creates instability from the bar [not static], learning to be controlled and stabilized and not allowing the bar to swing back n' forth as you go through the motions, effectively building several different groups of stabilizer muscles within the back, shoulders and arms. Having the bar set up this way forces you to learn great technique and can allow a greater 'time under tension'. Also, all the pulling/grip work with this setup directly translate over into my grappling/bjj. I will usually keep at this 4 times per week, with 3 days rest; do this format for several weeks then gradullay switch things up.
I also spend alot of time hiking around the areas here, lots of huge ravines, hills throughout the wooded areas here. Might end up being out there for 3-4 hours hiking. I've did this for such a long time that it's pretty much became an inescapable aspect of my life. 3 times per week I'm usually out in the woods at some point.
Man.. I could go on about this stuff. Definitely a huge potion of my life. The single best decision I ever made in terms of my life and my overall health. Any questions about any of this just ask. <3
Hope you stick with your new found endeavor!