Why does US equities valuation have the downward pressure on USD?
I think what your quote is trying to say is: Investors have bid up US stocks to the point where their valuation ratios (e.g. pe) are high relative to other countries. This could lead investors to rebalance in favor of other stocks. Hence the downward pressure on the dollar.
Whether or not that argument makes sense is another questions (about which I have my doubts).