I think it is a stretch to presume that without DARPA there would be no internet (or equivalent). There were many other networks that had nothing to do with the government - FidoNet, BIX, Prodigy, CompuServe, MCINet, innumerable BBS systems, and even I designed one in my head before I'd ever heard of Arpanet. Everyone who had two computers thought of connecting them together (and often did, with existing or ad-hoc protocols).
That ['DARPA created the Internet'] wasn't the point they made though.
If anything I think your "many other networks" example reinforces the point. The private sector left to its own devices came up with tons of incompatible small networks all vying to be the juggernaut.
The government, when faced with much larger problems than growing market share, instead invested considerable resources into solving a problem in a way that could handle the needs of a large national government, and then later invested more resources into making that internet a public good.
Even if the government hadn't developed its own internet protocols (and standardized on a notional private sector one), the government would likely still have been instrumental in expanding the use of some other standard. E.g. Eisenhower didn't invent the road, but his Administration sure did ensure a lot of them got built.
Putting aside the fact that the minicomputers that ran the early CompuServe came out of a multi-decade period of government-supported development and procurement, and also ignoring that CompuServe, Prodigy et al ultimately failed while the DARPA-spawned open Internet succeeded... the Internet is only one of a long list of technologies developed by DARPA or other government agencies over many decades and many billions of dollars. I mentioned just two in the headlines right now: Siri and self-driving cars, both of which trace directly back to taxpayer-funded research. Silicon Valley owes much to Big Government spending.
"What if" discussions are always ultimately flawed because one cannot go back in time and try something different. But my point is absent DARPA, the internet would have happened anyway in all likelihood.
Just like if the Wright Bros had not invented the airplane in 1903, someone else would have probably within 5 years. We'd still be flying today.
I suspect that the number of inventions that would not inevitably have happened once the preconditions were in place is very small.
After all, as I mentioned previously, having worked extensively with computers before the internet, the first thing someone with two computers tries to do is hook them together.
Hell, I even did my own hardware and software to transfer files from my LSI-11 to a PC over a wire. The government couldn't have stopped an internet workalike from forming if it tried.
