I know they have a larger range of services, but are they 20x the breadth of services? Think of what other companies do with 600 tech people and compare what the profitability per employee should be at an tech organisation of such a scale.
In a true software firm, more capital invested in headcount loosely means more features which is what drives sales. Here you can attribute a per employee profitability. When you hire more employees at a tech firm, the expectation is that you become more profitable.
At a non-tech company like a newspaper, technologists are a cost centre, you invest in technology in order to be more efficient, and hire as few people as possible.
Of course some technologists at the NYT will be profit centres. like those who work on advertising operations and games. But the NYT at its core is a news firm, it makes money on its influence and prestige which is driven by its journalism. Writers and content creators are the profit centres, everything else is a cost of doing business.
NYT annual revenue is $2.47B (https://stockanalysis.com/stocks/nyt/revenue/) with 5,900 employees. $150M/yr, 600 employees for their Tech headcount doesn't seem like a huge proportion.
Edit: Avg Revenue/Employee is $425,170