It is not outputting a fixed 12V if it's dimming an LED strip. Adding an inductor and capacitor is expected, standard practice on LED drivers.
Of course it's not outputting a 'fixed' 12V - that's the whole point of a PWM dimmer - the
average DC output varies as a function of the pulse width however the 'peak' voltage still remains at 12V hence the LED will always have sufficient forward voltage to conduct (emit). Current is still limited by the series dropper resistor.
The most basic PWM LED dimmer you can get is based on the 555 - and it doesn't use any any inductors. Nor is that a requirement of such a controller.
Are you 'conflating' the 'M' (modulation) part of the PWM statement? True, the PW signal is not 'modulated' (i.e. controlled by an external or feedback signal) so the 'M' bit can be argued - but that's just nitpicking.
I suppose the specific designation would be 'variable pulse width controller' but I've never seen it TLA'd as 'VPC' - they've always been known, if even colloquially, as PWM.