Your error is you are looking at the price of gold as fluctuating, and the dollar as being stable. That's nonsense, an ounce of gold buys about the same now as in 1900 - a good suit. Homes similarly cost about 200 ounces of gold (more in high demand places).
While we were on the gold standard (even nominally) the price of gold was artificially low (or, rather, the cost of dallars artificially high). So, when that constraint was removed, the dollar found it's true market value (Carter's "stagflation").
Since the dollar has again been wildly inflated with price manipulation of the gold market, that inflation will sometime show as a decrease in purchasing power of the dolar, while gold retains value.