I recently got a new mkiii and it had this adapter
Actually, what you have looks like that adapter in that picture, but it is different. The adapter on the MKII shown above is 2.5mm trrs to RCA female, and the adapter on the MKIII is 3.5mm (1/8) mono to RCA female. The MKII has 3 black bands on the 2.5mm post and the MKIII has 1 black band on its 3.5mm post. They are not interchangeable. The picture I showed in my post is not what comes with the deck, it is to show you have options, because on the MKIII there are lots of easily substituted replacements, which was not the case on the MKII.
The picture shown has the cable on the side so it is an MKII. The MKIII has the digital jack on the top. The cables look the same, but up close you can see they are different and not interchangeable.