You're modulating the DC (at an audio frequency) not RF.
You're confused and simultaneously confusing, as usual. Let's clarify.
Forgetting about which circuit we're talking about for a second, if you modulate the DC that is fed to a final amplifier, then you will amplitude modulate the signal. That's pretty fundamental. You can do this with a Class-A modulator, such as shown here or you can do it other ways, like a Class-D modulator and LPF. Either way, you're making the DC fed to the final amplifier wiggle up and down and that produces amplitude modulation on the RF at the "wiggle frequency".
In the case of the circuit from the OP, it only produces RF (without AF modulation, unless the RF already has modulation on it) riding on the DC. In the case of the second circuit, the one that I posted, it probably won't work very well at RF because it needs an inductor that the first circuit has.