I lack the economics knowledge to do more than parrot the response I've heard to this, so take this with the appropriate level of "hmmm":

As I understand it, the counter-claim is that the measure of GDP mostly excludes exactly the set of things that grows absurdly fast.

For example, the measure of inflation may include the cost of a smartphone in the standard basket of goods, but not the fact the GPU of a smartphone (or Apple TV) of today, operating in double precision mode, can do more than the Numerical Wind Tunnel supercomputer in 1993 costing 100 million dollars.

Or that everyone has a free encyclopaedia a hundred times the size of the Encyclopædia Britannica.

And maps which for most users are as good as Ordnance Survey, but free and worldwide, when the actual OS prices for just the UK is… currently discounted to £2,818.17, from £4,025.97.

Or that getting you genome sequenced now costs a grand rather than 3 billion. Although that might not yet even be in the basket, I don't know where the actual baskets of goods get listed in most cases, and search results aren't helping — one result, on a government website, lists "health", but even digging into the spreadsheet didn't illuminate much detail there.