What the sticker sayeth is the truth. The device is designed to be terminated into a load of 50 ohms (50R) at the antenna connectors. If the emitted RF power of the transmitter is not absorbed external to the device, the power is reflected back, which causes excess dissipation (EE speak for fries) the TX amplifier. The resulting standing wave patterns may also load the LNA (low noise amplifier, on the RX side) beyond its design limits (again, fry)
Antennas of course are coupled to the free space at . I know, shocking… - an impedance of 50 ohms.
Without antennas the proper way to test these things is with a 50 ohm (yea, that word again) dummy load. Sold separately 
In may experience WiFi kit is fairly rugged, however whatever damage occurs may not be easy to detect - rarely do these components fail totally, but what you will experience would be loss of TX power, loss of RX sensitivity, increased RX nonlinearity and noise (SNR+D).
I would not turn the device on without a termination or an antenna attached to all RF outputs. Sorry, could have mentioned this earlier in the thread, but in my mind this is something “everyone already knows.” Assumptions always come to bite you
just a little EDIT: If you decide to purchase termination, they are usually rated for power (Watts) - any of them will do. The ones you usually see sold in Western countries are mainly for measurement use, so they are exact to at least 0.1%, and priced accordingly. For this application of course this is unnecessary, so turn to whatever the local equivalent of aliexpress/banggood is. I haven’t purchased from them directly, but have seen them many with all of the usual wifi connectors.