I can now answer the question myself, as I simply ordered such a small magic box - and was rewarded: Yes - it can also be used merely as a router for a local wifi.

The device really supports all conceivable configurations:
Router (i.e. with private wifi for all connected devices).
access point
Client Mode
Repeater Mode
WISP mode (simultaneous wireless ISP access and sharing)

The device was configured exclusively as a WLAN client and used to connect wired devices to the wireless network. In principle, any WLAN device with router function should be able to manage a local network even without an Internet connection. However, I did not test the TL-WR802N for this purpose.