Moss tends to grow where other plants can't, namely wet or compacted soil, acidic soil (low pH) etc. They are surface growers without roots.  There are multiple ways to remove the moss, both toxic and non-toxic. 

We wouldn't use the Brush Killer. 

Has light power washing been tried yet? Soapy water and a push broom or edge?

The problem is that we expect it will return unless you regularly clean it or do something to change the area beneath the court, like having a drain installed.

We don't have expertise with play courts and suggest contacting the court manufacturer, like this one, for their thoughts:

www.sportmaster.net/maintenance/#:~:text=2%20parts%20household%20bleach%2C%20mixed,usually%20sufficient%20for%20general%20cleaning. 
The Brush-Killer is most appropriate for invasive plants and vines (which you can cut low and paint the herbicide on with a sponge brush). You may have some good natives in the area that you may want to keep- if you send photos we can help you identify. In the meantime, here is our page on invasive plants:

https://extension.umd.edu/resources/yard-garden/invasive-species/invasive-woody-plants

and https://www.invasive.org/alien/pubs/midatlantic/midatlantic.pdf

How close is your well? How deep? Used at a distance from a good depth well (some are hundreds of feet deep) you should be o.k.

You may feel most comfortable checking out the active ingredients in any pesticide/herbicides you use by contacting the National Pesticide Information Center- both their website info and phone line: http://www.npic.orst.edu/

No matter what, ALWAYS read and follow label instructions carefully and completely. The label is the law.

Christine