Seems to be neither SPI nor I2C
No, it's much simpler.
It does not have a CS pin and usess 2 clocks, the system clock at 2,5 MHz.
No, it doesn't have a CS pin, so the "bus" isn't sharable. What do you mean with 2 clocks? You have to provide it's chip clock, which is a simple rectangular signal, you can use a PWM for that. The SCLK is the serial clock, you have to provide an edge for every bit you wanna read. You can do this with 2 digital pins. So for the whole chip you need 3 Arduino pins, one of them has to be a PWM output with a free timer.