Variable Capacitor - capacitance vs. rotation angle
Rotary tuning capacitors are not necessarily simple sectors in their plate geometry.  Rather, more complex shapes are sometimes used.
If one wants linear change of frequency with respect to dial rotation, this cannot be achieved by linear change in capacitance such as caused in an angle-proportionate change in area.  Across a narrow frequency band it may be close enough, and in some applications the dial markings do not really need to be linear.  But for something like the local oscillator of a short wave communications radio, it was really quite important than dial markings correspond closely to actual frequency across the sub-band.
I've personally seen, and little web searching confirms, that more complex plate shapes with a slight teardrop character, plates offset from the axis, etc, were not uncommon.  A little care could yield a plate design to suit any reasonable desired capacitance curve calculated back from a desired change in resonant frequency.  Some examples can be seen at http://www.vk6fh.com/vk6fh/tuning%20capacitors.htm
(please don't edit to &quot;linkify&quot; that - as an external resource, it's meant to be only a supplemental example, and should it change the details of the URL such as the creator's amateur radio callsign may be key to finding it again)
As a practical matter, it's also critically important to note that an &quot;open&quot; design as shown in the question statement must sit behind a shielded panel, otherwise &quot;hand capacitance&quot; may distort the tuning.  More compact &quot;pocket radio&quot; designs such as actually used in the asker's kit presumably have built-in shielding; additionally broadcast channels are often wide enough that exact tuning is less critical than in some other applications.