How do I know when an amp has virtual ground?
There is no contradiction !
Ground is simply a reference point. The Cmoy amp needs +9 V and -9 V, the point "in the middle" is used as a reference and in this case also called ground. You could also choose the -9 V point to be ground and then the other points would be +9 V and + 18 V. But with the Cmoy amp you want to connect it to an audio source. The schematic shows how you need to connect the input signal of the Cmoy amp, the ground of the input signal (coming from the audio source) needs to be connected to the point between the two 9V batteries.

Virtual ground is a term used when an opamp is used in a feedback configuration with one input connected to ground and the other input is then a virtual ground since the opamp keeps it at the same voltage as ground but there is no physical connection to ground !

In the case of the Cmoy opamp there is no virtual ground ! I advise you not to worry too much about ground or virtual ground. It is not a big deal if you just want to build some design.

Just remember that ground is simply a reference point, nothing more than that. And virtual ground is when an opamp has feedback and one input is connected to ground, then the other input is called a virtual ground.