What many people seem to be missing (and it is totally normal to do so because it's not been seen before) is they keep comparing it to existing solutions.
SDC has something completely new in that it destroys coins that are then converted into redeemable tokens that sit on top of the blockchain and these tokens can then be reconverted via minting into new SDC.
It's only the exchange / allocation of tokens that use the ring sig with basic NIZK to prove to the blockchain that the holder owns the value of the output without revealing identity, it's not the actual coins using ring sig.
It is indeed a very well thought out system that the cannot be followed on an explorer.
First of all, every single cryptocurrency destroys coins when they are used. That's how the work. An input can be spent once and only once, and any output (including change) is a new coin.
What SDC has is essentially two types of coins on the same blockchain. When you say "destroys the coins" what that really means is a type of transaction that has one type of coin as input and another type as output (SDC calls this "mint" I believe). The latter kind is what is virtually identical to cryptonote. The former is (as far as I know, and I will assume this, but I haven't studied it) virtually identical to bitcoin. There is also a transaction type that has cryptonote-style coins on the input side and bitcoin-style coins on the output side (SDC calls this "redeem" I think).
This is indeed something new, and there are some advantages to it, but also disadvantages. It is not correct to say that it adds anonymity though.
The anonymity comes from the use of cryptonote style coins. As long as you use the cryptonote-style coins exclusively or predominantly, you have the same anonomity as Monero. If you mint and redeem frequently, you will have issues that reduce your anonymity.
Doesn't the anonymity come from the use of ring signatures? It's just that both Cryptonote and ShadowCash use similar simplified applications of them? And that Cryptonote did it first? That's an important thing to clarify and will help with discussion.