Liquidation preferences do not drive up valuations. Of course, they offer "insurance" to preferred stock investors against downside risk. But they have being so for several decades in the Valley (and elsewhere) and this has nothing to do with valuations as such.
Indeed, when valuations are at their very lowest (such as post dot-bomb in the early 2000's), the liquidation preferences became so high as to be regarded as absurd (e.g., 3x or even higher). This was often coupled with the idea that the preferred stock would be participating, meaning that the investors in any M&A deal get their 1x (or 2x or 3x or whatever) back and also get to take their proportionate share of the merger consideration on the M&A deal itself.
The reason there are $1B+ valuations is primarily because the VCs believe the ventures will come to dominate major areas of commerce, will typically go public with sky-high valuations, and will continue to grow and dominate even after all that. Investing $100M at $1B valuation is risky but pays hugely if the company later becomes valued at $100B+. Yet, when a company goes public, the terms of the preferred stock typically require conversion into common stock and, in that case, the liquidation preference goes away altogether and confers no benefit on the investor.
In short, very incorrect analysis and not really worth reading.