I think the tweet linked to by OP is using the colloquial definition of productivity (i.e. I can get more stuff done) and uses examples of computer technology etc.

This isn't to be confused with the economic definition of GDP per hour worked - which has far more to do with the sectors of industry that a country has.

After all, a few financiers doing million-dollar deals is always going to generate more GDP per hour than coltan miners, even though it's not obvious which is actually generating more wealth. Robert F Kennedy famously said the GNP "measures everything in short, except that which makes life worthwhile".