How does an additive like aluminum oxide make a material like polyurethane harder/more resistant to wear?
Alumina is extremely hard and very wear resistant, likely harder than anything which would come in contact with the floors. Dirt for example would mainly contain silica based abrasives which are far softer than alumina and hence alumina additives, of sufficient size would provide scratch resistance when present in sufficient quantities. 

If you want the exact details, they are going to vary from one manufacturer to another. If you do a search for patents you can see various procedures some of which are pre-mixed, some of which require onsite mixing, for example :

Surface coverings containing aluminum oxide

That kind of post-mixing is very common in concrete, though there the aggregate usually isn't alumina (could be just decorative as well or dual purposed as is common locally) and is far bigger. In general you want the aggregate to be at least as large as, and ideally bigger than the particle which is trying to cut it. If the aggregate is much smaller it won't resist wear strongly as it will be plowed out with the substrate. 

Effect of abrasive particle size on abrasive wear
of hardfacing alloys

If you are curious about a specific product then just call the manufacturer and ask to speak to the engineering department. However as they are all likely patented products, you can even search manufacturer specific and turn up results.