There are various reasons behind what you're seeing, and most of them are due to the differences between those pieces:
The first example contains a “small” ancient music ensemble. But don't get confused by the concept of “small”: actually, for ancient music, that's rather big, it was only in the last 2 centuries that standard orchestral instrumentation has increased in numbers, with pieces requiring even hundreds of musicians. Up until 1800, orchestras rarely had more than 40 players; in previous centuries it was more common to have small ensembles and chamber music was more popular and performed.
Having a large orchestra also means that large groups of its players play the same thing (unison), especially in strings, while in small ensembles almost all instruments have their own part that is not doubled by any other.
When you're the only one playing your part, you have more “room” for interpretation, and more interpretation often leads to bigger movements, even if they are not directly related to those required for playing. Have a look at this, for example:
As you can see, the soloist is doing a lot of movements.
This is somewhat important for performance, as any body movement has a partial role in the resulting sound and expression. You shouldn't move too much, but you shouldn't stand completely still either.
If you look closely at the second video, you'll see that wind instruments actually move a lot more than string players, and that's also for similar reasons.
Playing the same parts as other musicians also means that you have to “play less” (be aware, this doesn't mean you play less notes or you play with less emphasis).
Another aspect depends on the speed: controlling an instrument demands precision, and playing fast music requires faster control on the instrument, which could be a problem if you move too much.
Also, the type of instrument creates physical differences that allow or require more movements.
There's also other related aspects to consider for the ensamble: when lots of people move in the same way (since they're playing the same thing), the overall perception of movement is less, and the musicians also actually have less physical room – which also means that they shouldn't move too much, or they would distract their colleagues.
Finally, and you can clearly see this by comparing the video above with your first example, playing while standing up (which is common for ancient music ensembles) allows you more freedom of movements.