I don't know a whole lot about how joysticks work, but since they're analogue I don't think wiring one up to the arrow keys like that would work anyway, even if it were connected properly to the corresponding rows and columns.
Maybe there was some external button connected to the jack that was wired to the asterisk key? I wonder what the intended purpose was.
The picture of the switch is too dark to make much out, but it looks like it might be a 4 tab clone switch and not actual Alps, which seems to correspond with what the FX designation usually meant.
(Attachment Link)
Ortek used a few different kinds of clones in their similar boards.
I confirm what you supposed, this keyboard indeed has the 4 tab clone switches.
As for the joystick (getting out of topic here), it is branded "Zipstick". These joystick have an Atari joystick connector and they are compatible with Atari 2600. It is interesting because i also got an Atari 2600 at my grand-parents and i'm pretty sure this joystick was intended to be played on it at the time.
Most likely my grand-father cut off the connector to have the joystick soldered on this keyboard later when he got into computers.
Anyway, this joystick is not an analog one, it consists in 6 switches :

I still need to check what is the other connector all about.