>The emergence of the state probably could not have happened without writing.
Empirically speaking the opposite is more likely - writing emerged from state accountants keeping records of grain etc. Writing was independently invented by several states across the globe, in fact.
>Steam engines and machine tools could not have happened without the printing press.
Why's that?
This is a very hard subject to discuss, because steam engines and the industrial revolution (I mean precisely the shift from an agrarian economy to a mineral economy, i.e. the switch to using non-living energy sources) happened exactly once, in the UK, and spread worldwide from there. It's hard to extrapolate from a dataset of one.
However, from what I understand of the industrial revolution, it didn't strictly require the printing press - the core driver was of needing to extract coal from a deep coal mine that was flooded; because the coal mine produced a bunch of low-grade coal that was disposed of onsite by burning it (because it was too crappy to be worth the transport costs of selling it) the efficiency of the steam engine didn't matter because the fuel was free.
There were a bunch of implicit requirements (the obvious one being the demand for coal) that are extensively debated, and while we could speculate the printing press was helpful in some way, I don't see any reason why a printing press would be a hard-requirement.
>Networking (telegraph) was the predecessor technology of computers.
The Antikythera mechanism predates the telegraph by millennia. Computing was orthogonal to networking for the majority of its history.