Yeah. The flip flop, and its corresponding register version would be a DFF with enable pin. That is not actually too abnormal. The traditional implementation is taking a normal DFF and adding the enable feature either by gating the clock or by adding a mux in the input path, that uses the enable signal to select between the input or the existing output.
Everything started making sense after I thought of "store" as "enable", and I made it to the end pretty quickly after that --- except for the "bonus" multiplier level, which is definitely possible but seems like it would take about 10x as much space as the canvas allows.
