What is the relationship between the Komodo coin and the decentralized exchange?
Or in other words - what will determine the demand for KMD?

Why does/would one of those things have to do with the other? Komodo creates the demand for Komodo, with or without BarterDEX even existing.
I believe in barterDEX. But why should I buy coins KMD if they do not have a connection with the exchange?
Many investors are interested in this questions.
The DEX is but a tiny, fractional part of what Komodo is, does, and offers.
Saying that you'd only hold KMD if it's required for the DEX is akin to saying that you'd only buy stock in BrandX car maker if you can leverage that stock to buy a motorcycle from them, but only if that motorcycle has a round emblem on the fuel cap.