I saw a lot of simple peak-current-controlled discrete-transistor oscillators like those, when taking apart LED bulbs as a "competition analysis" at a previous job - you can save a lot of money in volume by just adding an extra winding on your inductor and having no control IC. One kind-of-rough way to do voltage feedback, when you don't need tight output regulation, is by peak-detecting the reflected output voltage on the primary side of the flyback through an auxiliary winding - see the first attached schematic for an example of an off-line supply that does just that.
There's also another simple off-line power supply I traced a while ago which is probably almost identical to yours: it does exactly what Tim describes (see second attached schematic). You can see in both cases how they're arranged as a flyback, with a second transistor that has its base connected to the current sense resistor. This terminates each switching cycle at a specific peak current, when the current sense voltage becomes high enough to turn on that second transistor. The turn-on then happens again via the auxiliary winding of the flyback inductor, and a resistor & cap from it to the base of the power transistor: when the flyback current ramps down to zero and the voltage starts to ring in the opposite direction (the "L" of the windings & the Coss of the power transistor form a nice series-LC circuit), that voltage reversal on the auxiliary winding provides a turn-on voltage to the power transistor ...as well as some positive feedback so that once it starts turning on it turns on HARD, and vice versa.
To control the converter, the peak current threshold can then be shifted downwards by variable amounts, by doing some resistor-based voltage summing at the base of the peak-current-sense transistor. The simplest way is to have a zener diode coming from the reflected-output-voltage-sensing, so that any conduction through the zener lowers the peak current threshold. The sketchy supply actually uses a more accurate output voltage sensing (again, exactly as Tim describes) with a TL431 doing voltage regulation on the secondary side, and driving an optocoupler which provides variable current to shift that peak current threshold on the primary side.
Hope this answers your question. Happy to explain more details if you're curious about exactly what each part of the circuit is doing - I got deep into this for a little bit years back both to compare the component-by-component optimizations that other lighting manufacturers were doing (some of these had pretty sophisticated temperature foldback & "dim to warm" color-temperature adjustments, implemented all with a few discrete transistors), and also partly because these types of circuits made for great "weed out the people not suited for R&D" interview questions at work, watching engineers try and work through how they functioned.