WordPress support
WordPress, as a PHP application, can run on PHP WebAssembly. However, there are a few caveats.
SQLite
First, WordPress requires MySQL. However, there isn't a WebAssembly version of MySQL you could run in the browser. WordPress Playground, therefore, ships PHP with the native SQLite driver and leans on SQLite.
But how can WordPress run on a different database?
Behind the scenes, the official SQLite Database Integration plugin intercepts all MySQL queries and rewrites them in SQLite dialect. The x.0 release ships a new WordPress Playground-informed translation layer that allows WordPress on SQLite to pass 99% of the WordPress unit test suite.
WordPress in the browser
You can use any WordPress build in the browser. For convenience and to reduce the data transfer size, WordPress Playground ships a few minified WordPress releases that you can use in the browser.
WordPress in Node.js
In Node.js, you'll typically want to mount WordPress from a disk directory.