The actual list of supported radios depends on the hamlib version, not Cqrlog itself. You can obtain the actual list using the command terminal with:

rigctld --list

Remember, the rigctld executable must be on your path that it usually is after installation.
There's no standardized protocol to remotely control one's rig, be it a Ham radio transceiver, a SWL receiver, any kind of scanner or other mobile. Many manufacturers have designed their own proprietary protocol, implemented in some of their product family. Therefore, each rig family will require a Hamlib backend to set the VFO frequency, change mode and passband width, get current signal strength, etc.

Communication between Hamlib(rigctld) and Cqrlog is standardized and when Hamlib supports your rig Cqrlog will also support it.
Note that with Hamlib, as well as with Cqrlog, package maintainers very often offer old versions to install. That's why it is recommended to compile both from source code that is available from github.com. That way you will get the latest versions for use.
https://github.com/Hamlib/Hamlib
https://github.com/ok2cqr/cqrlog

Note: If your radio is not on the list, it does not mean that it is not supported at all. The Elecraft K3 radio works as K2 (Rig# 221), you could also try one of the Kenwood radios. The Ten-Tec Omni-VI uses the Icom IC-735 backend.