Percentage of GDP seems like a really awkward measure. Government takes dollars to run and budget makes for a good approximation of size. With GDP, imagine someone invented an amazing technology that 10x'd the GDP of a country. Would you expect the gov budget to 10x in line? That would seem like a terrible capture of resources.

(imagine say, the internet, etc)

It still measures effective ROI - and traditionally growth in GDP is accompanied by growing needs. It is true that it is fuzzy - different needs scale differently as well. A 10x GDP rise would almost certainly cause an explosion in demand for other services as well with or without the influx caused by the growtg.

That chart shows government spending at about 35.8% of GDP in 1980, and 37.8% now.

Indeed. I totally misread the chart. Edited my post to reflect the error.

In my defense, I think it still shows something quite different from what the OP was claiming. But I was even more clearly wrong.