I'm pretty sure that's not how productivity is defined. I can't read the article, so I can't tell whether your "productivity = wages" is a definition they use, but that would be a very odd definition.
Productivity is usually defined as total output of the economy, not the fraction of it that got paid to workers.
[Edit: Per a quoted snippet from another commenter, it looks like it's total output divided by hours worked. Still not wages, nor closely correlated.]
It's not perfect, but it's a good proxy that you can calculate from macro figures without needing data from every single company etc.
Profit per hour worked (which will be somewhat correlated) puts a hard ceiling on wages, so it is important.
It's more to do with the type of industries a country has. The USA has many of the world's largest and most successful corporations and their HQs generate a lot of highly productive and well-paid jobs.
Meanwhile Southern Europe, for example, depends heavily on tourism which creates less value and tends to have low paid jobs.
The thing about how Europe has no Big Tech companies is almost a meme. But it has some truth to it.
aka wages in an economic sense