I've done a lot of these at various times. I got hyped up about them when the Matt Furey book came out and have returned to them periodically, building up to over two hundred in a set and over a thousand in a day.
Not at all similar to swings. Swings are an explosive hip hinge, and Hindu squats are, well, squats, and driven by knee flexion/extension even more than a regular flat-footed squat.
I think Hindu squats are a good complement to swings and other squats because they do stress end range knee flexion in way that other exercises do not. However, I think they should come with a couple of caveats.
--They do put a lot of stress on the knees in an extreme range of motion. Some people may not tolerate this at all. Most people will need to build volume very conservatively (as in do WAY less than you are capable of) and use a deliberate, smooth and controlled pace (not drop and bounce).
--I don't think they are a great choice for generalized "conditioning" (whatever that means), since fatigue is very localized, and going hog wild on volume and pace will likely lead to achy knees (guess how I know this).
I would add them (if at all) in small doses, as a fill-in-the-gaps complement, not as a focus of training. For a lot of people, Hindu squats are a "dose makes the poison" kind of thing.
A loaded version of the Hindu squat that I like is the KB hack squat, which I believe is described in Beyond Bodybuilding. Basically, you do a Hindu squat while holding a KB behind the back. The key to these is keeping the torso upright; leaning forward is a cheat that make the drill very easy. With an upright torso, you have to keep the glutes very tight and really drive the hips forward to get out of the hole. The same caveats about conservative progression and non-tolerance apply to KB hack squats as well.