Hi you send your btc to a multi sig address that's distributed over 3 or so servers. Then after 6 confirmations you get mgwBTC asset and you sell/bid/ask that for nxt on the asset exchange. Trades take as long as nxt blocks. Look into instantDEX for real time decentralised trading. 
So the trades at mgwBTC are not instantaneous? Also, how the distribution of bitcoins between 3 (or more) servers helps prevent robbery? It may make it more difficult to steal all the bitcoins from all the servers, but this still doesn't prevent server hacking AND stealing the funds, if I'm not missing something. My point being that I lose control over my funds once they are sent to the exchange. Is this not what decentralised exchanges are supposed to get rid of?
Trades of mgwBTC (on Multigateway > MGW), are not instantaneous. InstantDex (which makes use of MGW) is designed to be (testing next week, proof of concept showed 3-5 sec).
The three servers don't split the BTC, these are split among many accounts (proportional to the amount of users, IIRC). There is no huge hot or cold wallet. The three server operators only confirm transactions, using multisig. All three have to be in agreement before a transaction takes place. It have increased the point of failure from corrupting 1 server/exchange owner to 3. 1 server operator can't do anything on their own. I would call MGW a distributed or 'most decentralised' exchange at the moment, InstantDex is designed to be truly decentralised.
When you send 1 BTC to MGW, you automatically get sent 1 mgwBTC. This is 'backed' by BTC in the true sense of the word as it is directly convertible back to BTC (which are spread between many accounts and protected by multisig accounts above). The mgwBTC are stored in your wallet, not on the exchange so you control the keys. And the coins backing them are protected by multisig.
If my real bitcoins nevertheless got stolen (or rather all bitcoins of all clients at the exchange), what purpose will these mgwBTCs serve to me? In fact, I don't see any real difference they make since my bitcoins are still at the exchange.
For instantaneous, rather than 'not centralised', transactions then I think you would be more interested in InstantDex.
Yes, I keep an intent eye on it, but I still don't understand the principle behind it. What puzzles me is how I can maintain control over my coins (the essence of a decentralized exchange as I see it) and at the same time be able to make instant trades. Could you expand more on this?