MSX Cassette cable
To record on a laptop that has a separate mic input, just grab pin 4 from the DIN with a ground (e.g. pin 8) and hook both into a mono jack that plugs into the laptop.
If you want to record on phone or a laptop with combined signals, the cable from your link has two 3-way plugs. It can load into MSX, but that won't work with recording. You need 4-way (TRRS):
Then figure out whether your phone/laptop is CTIA or OMTP standard:
and just do the right wiring. When done right, you should be able to see mobile audio recording programs indicating the presence of "an external mic".
If playback into the MSX isn't picking up any games, ensure your phone's volume is set to max before playing the cassette. Also, in MSX2CAS make sure you choose a proper playback speed that your MSX can handle. IIRC my AX170 was able to handle both the slowest and the doubled up speeds, but not faster than that.
