But is it also possible to trigger the remote flash using the built-in flash on my camera?
Or is this only reserved to TTL-compatible flashes?
No, it's not. There are two manual-only single-pin Yongnuo models that can be triggered as a CLS or wireless eTTL slave with TTL/HSS, etc.: the YN-560EX, and YN-510EX.
All the flashes in the Yongnuo lineup that can be "smart" optical slaves have EX in their names. But most will be the TTL models, because the difference between "smart" and "dumb" optical slaving systems is the ability to communicate TTL (and HSS, and settings changes, and...)
You can, of course, also use the S1/S2 modes on most of the Yongnuo flashes that aren't EX-designated, like the YN-560III/IV, etc. (pretty much everything except the YN-685). But this is a manual-only triggering system, and you cannot have TTL, HSS, or settings control, and you'll have to set the power level on the flash itself. But it will respond to any flash burst: even that of the built-in flash on a P&S compact camera.
The S1 mode fires on the the first burst it sees, the S2 mode fires on the second burst it sees (to skip firing early on a TTL metering pre-burst).
See also: What are the Yongnuo flash naming conventions?