Did the Nixon shock cause skyrocketing real estate prices in the US? Ca. 1970 the prices of real estate started skyrocketing in the US: Real estate prices chart. Same with gold: Gold prices chart.

So my conclusion is that real estate did not increase in value, it was the USD that decrased its value.

Further my theory is that Nixon taking US out of the gold standard in 1971 was what caused this. I assume that after this the US started printing a lot of dollars and paid down their foreign debt with the new less valuable dollars.
Looking at gold values is simply cherry-picking. From 1970 to 1980, the CPI went from 38.8 to 82.4, an increase of 112%, and an annualized rate of 7.8%. Your chart shows housing prices increasing about 200%, an annualized rate of about 11.6%. So while most of the price increase was due to inflation, there are 3.8 percentage points that remain unexplained. 

One can also compare the dollar to other currencies. While the $/£ rate fluctuated a lot in this period, from 1970 to 1980, overall the dollar actually strengthened against the pound slightly, and from 1970 to 1976 its strength more than doubled. The Yen exchange seems to show the opposite trend, however.