That's a simulation based on the connectome and a trivially simple body, producing a very small piece of behaviour. I don't mean to minimise it, it's very cool and I'm not an expert. The video itself says that it is limited.
As I understand it, C. Elegans displays a surprisingly large and complex set of behaviours given its (relatively) extremely simple nervous system. A database of thousands of these "behavioural phenotypes" has been built and provides a well-defined goal for attempts to reproduce the behaviours in simulations. Very few of these behaviours have been replicated. To solve the problem will apparently require a lot more than the connectome, which has been known for a long time. It's not enough to know that neuron A connects to neuron B, or even the full 3D structure of that connection. You need to know how that connection influences the behaviour of the connected neurons. People refer to this as "knowing the weights" but AFAIK it's still an open question whether a model based on "weights" is sufficient.
That model's phase space is about 2000 bits, realistically speaking its behavior never repeats. It can't be searched either, our computational limit today is about 70 bits.
I'm not clear what you're saying there. You shouldn't need to exhaust the phase space to check if the model exhibits a particular behaviour, but perhaps you're not claiming that?
The simulation derives behavior from the state of neural network, in order to produce desired behavior the state should be known first, in general case you need to search it if you don't have a reliable method to reach it from any other state.
