This is what I currently think will be needed.

1. The audio from the cassette player needs to be amplified and shaped in to a proper square wave.
2. The square wave will be decoded using either a PLL or simply a monoflop with a timeout set in the middle of the two frequencies.
3. The startbit of resulting UART-like serial bitstream will be detected
4. The startbit syncs a bitrate oscillator and resets the serial->parallel converter
5. The S/P converter receives and stores the serial bitstream at the rate determined by the oscillator and outputs this to a 7-segment display

The actual serial->parallel converter can either be done with a 8-bit SIPO Shift Register (pretty much like the 74LS595) or with 8 separate flip-flops/latches that are triggered one-by-one. The triggering can either be done with a 8-step ring counter or by a decoded 3-bit binary counter.

Seems easy enough ;-) But will probably need quite a lot of transistors