Stock market indexes are generally based on market capitalization, which is not the same as GDP. GDP includes the value of all goods and services produced in a country; this includes a large amount of small-scale production which may not be reflected in stock market capitalizations. Thus the ratio between countries' GDPs may not be the same as the ratio of their total market capitalization. For instance, US GDP is approximately 3.8 times as much as Japan's (see here), but US total market cap is about 5.5 as much as Japan's (see here).
The discrepancy can be even more severe when comparing "developed" economies like the US to "developing" (or "less-developed") economies in which there is less participation in large-scale financial systems like stock markets. For instance, US GDP is roughly 10 times that of Brazil, but US total market cap is roughly 36 times that of Brazil. Switzerland has a total market cap nearly double that of Brazil despite its total GDP being less than half of Brazil's. Since the all-world index includes all investable economies, it will include many economies whose share of market cap is disproportionately lower than their share of GDP.
In addition, according to the fact sheet you linked to, that index tracks only large- and mid-cap stocks. This will further skew the weighting to developed economies and to the US in particular, since the US has a disproportionate share of the largest companies.
Obviously one would need to take a more detailed look at all the weights to determine if these factors account precisely for the level of discrepancy you see in this particular index. But hopefully that explanation gives an idea of why the US might be weighted more heavily in a stock index than it is in raw GDP.