The term perfectly captures what I love about these games: exploration, taking in the environment, exploring and enjoying the world that the designer created, but doing so without pressure, without power-ups, without time limits, without having to have good reflexes, without getting stuck on difficult parts and ending up frustrated — in a word, without adrenaline.
To me, that is really what "ambient" means, but I think it furthermore implies a certain design of the world itself; artistically rendered, visually beautiful, filled with little touches and details, and never getting in your face, as it were.
Thinking more about it, BTW, I think most games I like have elements of this. My single most favorite NES game to this date is the original Legend of Zelda, and that's very much due to its huge world that was yours to explore, the lack of any mandatory objectives at any given time, the lack of such things as time limits for levels, lives, and so on.
Later on, I thoroughly enjoyed classic adventures, especially the LucasArts ones like Monkey Island 1 and 2, Day of the Tentacle and so on, also games that were very much about exploring and seeing an intriguing worlds (while solving puzzles, but although for some people, those were the essence of adventure games, I always enjoyed experiencing the worlds more). I think this also explains why adventure games that were more railroady (not to mention more deadly), like Sierra's many offerings, never appealed quite so much, at least until they started employing a more relaxed approach (perfected in e.g. Leisure Suit Larry 6); and it explains why I never got into games such as Crimson Room, Viridian Room etc., which eschew open-ended exploration in favor of a reduced, austere world and an exclusive focus on puzzles. That said, it's about the world more so than the graphics: Castle Adventure, one of the first computer games I had and played, was also great.
The German RPG DSA I: Die Schicksalsklinge, also a long-time favorite of mine, also fits in this; I never really cared so much about the overarching goal in that one, and instead preferred to roam and maraud. :) Unfortunately, in that one, there's a deadline by which you have to complete your quest and finish the game, or you'll lose — I found out the hard way, and never really enjoyed it as much anymore afterward.
Even Nethack, despite all its difficulty (for casual players like me) and deadliness, arguably fits into this. And don't forget about DOOM: I actually don't care so much about the adrenaline, so I usually just play in God Mode, and my favorite levels are those that are visually stunning, with beautiful architecture and lots of atmosphere. And let's not forget about golf games — very relaxed, very much about enjoying the environment. Sure, they were also about skill, but it's not as if you lost if you didn't hole in in less than X strokes.
Getting back to Knytt and ambient exploration in the strict sense, if anyone knows any further such games, I'd love to hear about them. (Ideally ones that are free, of course, or have a free demo. One that I just tried is a newer Nifflas game titled Knytt Underground, but after playing the demo for a bit, I found it too adrenaline-inducing after all; in a word, not ambient enough.