How do remote access devices work without a cellular connection or internet
...you can use this system independent from cellular networks because it sets up your own Wi-Fi hotspot similar to a wireless network in your home


It seems to set up a wireless adhoc (independent) network , to which other wireless-enabled devices like smartphones and computers can connect. (Note that this is different from connecting to an existing infrastructure network/access-point.) You can read the Wikipedia article on Wireless ad-hoc networks.

If you are asking because you're interested in setting up something similar, note that wireless module units with ad-hoc capability, are available widely, for example this one.