HDMI is 'the magic cable' in that it is capable of carrying all this information - picture, sound and control (oh, and 5V DC power) - but what happens to it is down to what the equipment at each end can do.
In the case of the Sony, the HDMI switching is of the 'pass through' kind, in that it can allow a signal through, and indeed switch HDMI from two inputs so that they're output from the single HDMI output it has, but the receiver can't extract any of the information travelling down the cable. To do that you'd need to look to the next model up the Sony ES range, the STR-DA3200ES, or to the new STR-DG910, along with some rival products.
In the STR-DA1200ES the HDMI pass-through is merely a convenience feature.
So yes, for audio you do need a standard digital connection from player to amp. That will deliver surround sound from DVDs, as well as stereo from CDs.
The bit about analogue cables from player to amp is based in the assumption that the player's onboard digital to analogue conversion is better than that in the receiver. In all honesty I should think you could skip those and just use the digital link for CDs, too. Otherwise you're going to be into another £30-50 for some decent analogue interconnects - I'd rather spend the money on a good but sensibly-priced digital cable, such as Atlas Element, Black Rhodium Rhythm or Ixos XHD-608-100, which are all in the £30-50 range.