The datasheet for TN266 actually does say to use ceramic caps. Page 7, or control-F "ceramic" and it is the only result.
On a broader note on how to choose caps: most cap technologies have their characteristics. Ceramic caps tend to have low ESR/ESL and therefore are nice to use as bypass caps for digital circuits. They also are cheap, so that's real nice. Film caps are not cheap; they are also big for their capacitance. They make up for that for having exceptionally low leakage, low tempco, high linearity and precision.
All C8 does in your circuit is bypass the internal 5.6V rail. You should be fine with basically any capacitor provided that you select the right voltage for it. I recommend something like twice 5.6V, just to be safe.
This is not to say any rail/regulator can be bypassed with any capacitor; some high-performance regulators require that the capacitive load have some loss (ESR) to remain stable. Always check your datasheets.
Also, if you want to be safe with your design, you should probably include a real fuse or a PTC, ensure C1 is an X rated capacitor, and C5 is a Y rated capacitor. X rated means a short-mode fail of the capacitor causes it to short out mains and is appropriately rated, and Y rated means a short-mode fail of the capacitor causes it to short mains to isolated "user" side.