As the top answer to this related question states, plants in general are oxygen neutral. In other words, whatever oxygen is emitted today will be emitted as CO2 later. So what really matters from a climate perspective is CO2 storage, not oxygen emission.
That said, short-term oxygen emission is apparently difficult to measure, but it is largely a function of leaf surface area. This extension site from the University of California states:
Assignment levels of oxygen emission are not precise and different
methods can give different results. That said, it is well documented
that oxygen release is proportional to the overall leaf mass, also
known technically as Leaf Area Index.
There is general agreement that:
- Pines are at the bottom of the list in terms of oxygen release because they have a low Leaf Area Index.
I can find lots of sod companies promoting the oxygen producing properties of their product, but no independent research supporting their claims. It is possible that immediate oxygen emission by sod is higher than pine forest, but as far as I can tell, the 10.000 m² is just a made-up and meaningless figure.