Have you got your inches and cm mixed up? 23cm x 16cm x 9cm is about the size of a box of cornflakes. If you mean inches, then that's 58 x 41 x 23cm which is indeed rather smaller than your other case and is 54 litres (multiply the three dimensions together and divide by 1000) which is half your extra large case.

It's hard to believe that a replacement case can be the same in exterior height while being 15cm less in interior height, but if it has the spinner wheels, you could well be right.

The problem is that suitcases are often sold on the basis of height - if you try to buy one on Amazon, that's how they are categorised - and you need to look in more detail to see how large they actually are overall (speaking from recent experience trying to buy a large suitcase).

I'd suggest
(1) calling K2 back and seeing if you can get someone who is a bit more numerate and explaining that you're looking for a suitcase with at least 120 litres capacity;
(2) if you do have to send it back and exchange it for a larger one, and you like the one they have just sent you (apart from its small size, and assuming any larger one will be the same brand), and they can give you full details and dimensions of any larger ones they have (including brand, model name, and interior capacity in litres, although you should check online at the manufacturer's or a retailer's website to confirm), then it might be worth £20 to get a new one on that basis.

Beyond that, not sure you're going to get much joy from BA, I'm afraid