It is sort of tricky to run spatial queries against tables in a GeoPackage anywhere, but especially outside of QGIS. This is because we're reliant on Spatialite to carry out those queries and Spatialite is just not well supported. A real shame!
Luckily there are a few resources for helping you get up and going with installing Spatialite for working with GeoPackages in a SQL client like DB Browser.
There is a page in the DB Browser Wik on GitHub called ["
SpatiaLite on Windows"](https://github.com/sqlitebrowser/sqlitebrowser/wiki/SpatiaLite-on-Windows) and it is dedicated to installing Spatialite for use with DB Browser. Note that there are special instructions for a Windows 10 issue.
Bryan McBride at Spatial Networks wrote up a nice piece on working with GeoPackages in DB Browser called ["Working with Geospatial Data: An Introduction"](https://www.fulcrumapp.com/blog/working-with-geodata/). It's got a nice walk-thru of how to use DB Browser with GeoPackage as well as some general installation instructions. They are better suited for Mac or Linux users.