If you have a NOW Day or full Monthly Sports Membership you should be able to watch on Demand Sports content where available.
Should you be using a Mobile Sports Membership then you won't be able to watch Sports on Demand.
My guess that the US Open Tennis will be available on NOW Sports on Demand, but might be worth waiting until the US Open Tennis starts on Sky from 28th of August to see if the matches gets added to NOW Sports on Demand.
I am hoping NOW will provide a dedicated NOW on Demand Tennis Sports category like they have for Football, Cricket, Motorsports, Golf etc.
Currently there is some old tennis matches on the NOW on Demand service.
If you open the NOW App and click on Sport very top line of the App main screen, then navigate down to the bottom of the Sports screen page, then click on Sky Sports Action, Sky Sports Arena and possibly Sky Sports Mix where the old tennis matches are spread currently across these three on Demand channels.
Hopefully NOW will create a dedicated Tennis on Demand folder category before Monday so all the tennis on Demand is in one folder place, instead of looking through these three Sky Sports channels on the bottom of the NOW App Sports section.
If you have a monthly Sports Membership already, then perhaps try watching one of these old tennis matches has a dry test run.
Maybe start with the NOW App on your TV and then try the NOW website with your Laptop.
Since I checked last earlier this week, NOW have moved the old tennis matches from Sky Sports Action into Sky Sports Arena on Demand.
Where Sky Sports Mix only has roughly two or three tennis related folders for on Demand viewing.
A dedicated Tennis Sports category folder would make things much easier to find when it comes to tennis on Demand.