Upon investigation it seems that Rich content does not rely on site styles. I am not personally sure if this is by design or a bug. If you would like to report the issue as a bug for investigation, you may do so here Wix Studio - How to report a bug
Now - if you want to attempt a workaround in the meantime - you may be able to accomplish managing this font through media queries and css.
Alternatively, there may be solutions on the app market that will be easier to implement. I briefly searched and saw this one (untested by me) Snippets | Wix App Market | Wix.com