"Algorithmically defined" doesn't really mean anything. The redemption price could be floating based on the BTC balance for the side chain (for example a minimum conversion price "algorithm" of 1/balance would ensure that the balance never ran out).

Side chains aren't really that different from a decentralized exchange (in fact the atomic swap concept is exactly cross chain trading) except that in the original conception the expectation is for a fixed 1:1 exchange rate. I don't see anything that requires that though.

I think it may well turn out that side chains are just a reinvention of altcoins.