Probably setting up strong, well paid and well monitored police force would be sufficient to provide secure environment for the business.
And some of them (even under the "no armed forces") list actually have a military from the descriptions there, its just a reserve military, an armed police force officially designated to serve military/defense functions, or, in the case of the State of Vatican City, the military of the entity -- the Holy See -- to which the state is itself subordinate.
These investors would have a direct stake in propping up the idea that this is sovereign land, as that's what will give them the best return on their investment. So the new ruler and the investors form a tight bloc.
The whole idea is to make the area attractive to commerce, once the businesses start coming in, and the people to run and operate the businesses, then there's a critical mass to begin the process of drawing up a constitution, figuring out how to set up legislative bodies, the machinery of governance.
Only after all this is done is international recognition needed.
The reason micronations never got off the ground is because nobody was ever able to court enough investment to build up to that critical mass that can support commerce. They were just way too small. City-size seems to be at just the right scale for this kind of experiment. It was just a matter of time until something like this happened.
Note this is also the exact same process whereby new townships are formed in the US, particularly in the 1800s where we were in our expansionary period. Only they don't have to set up the full machinery of state, they already have a state and federal government to build off of.
Eventually somebody is going to get this right in the developing world, and that will kick off a hoard of copycats. As regimes topple, people will start breaking these countries up into city-states. Think of how gentrification works in the US, if you think about it, it's just the process of cities growing. Sovereignty in the developing world is going to follow the money.
But in Kaliningrad's case it used to be attached just fine to the rest of Soviet Union from which Russia "inherited" it.
No part of former Yugoslavia was ever close to bordering Russia. At least not yet :P