"It's an independent, portable and free project, aiming at being compatible with AmigaOS 3.1 at the API level (like Wine, unlike UAE), while improving on it in many areas."
IMHO likening AROS to Wine is slightly misleading. True, it is more correct than comparing it to UAE, but still quite a bit off. What AROS provides is a API compatibility (and potential ABI compatibility on m68k hosts). Wine provides both API and ABI compatibility (and thus obviously only works on x86).
Do I understand then that the goal of AROS is to run Amiga games and programs without emulation
No. AROS does not run amiga games or programs. You need to use UAE.