What Gurley is referring to here is actually a level higher up than VCs. He's talking about the people who give VCs their money - Limited Partners or LPs.
LPs are usually very high net worth individuals or funds who invest a portion of what they have in venture funds. VCs are the people who get paid for managing those funds.
If you're responsible for managing the Harvard Endowment Fund (which is larger than the GDP of most nations) you're going to be investing large chunks of capital, and you're going to try and diversify the way you invest it. Say you put 20% into commodities, 30% into real estate, 40% into mutual/hedge funds (the stock market) and 10% into tech via VCs. (Of course, these numbers are complete bogus.)
If the market shifts and all of the sudden you expect really low returns from some parts of the economy, you may shift that money into other parts. So instead of putting 10% into tech you might bump that to 20%.
If that happens across the board VCs will be flush with cash, but unless there's a systemic change in how companies are starting they'll still be responsible for dumping that cash into companies. Remember: if you're a VC it's literally your job to invest the money the LPs give you.
All of the sudden every VC has tons of cash and there aren't enough good companies to invest it in. You might as well invest at really high valuations in the quickly growing companies: It's either that or taking bigger risks on lower quality companies. (Gurley has argued that both of these things are happening, but in this article he's more specifically arguing the former.)
The assertion Gurley makes is that now the market is starting to correct itself a bit. That correction takes place when either the returns are low enough that LPs stop investing as much of their capital in VC or if other investment opportunities heat up and LPs abandon VC to some extent.
Interest rates haven't gone up, so it's not like there's money moving out of VC to make other particularly great investments, but companies aren't being bought very quickly or going public. This means VCs aren't able to give cash money back to the LPs. Therefore the LPs can't reinvest this cash in new companies, and there's still some level of skepticism around whether these companies will return what they're "worth" on paper at the end of the day. If they put less money into VC the companies raising money will have a harder time doing so. Gurley is arguing that this is happening now.
Overall VC is a minuscule part of the overall economy - it's basically a rounding error - but how much money is in VC is very much dependent upon how other parts of the economy are doing.