Jeff, how did you get them to run in the browser on a single click? I would've thought the JRE needed permission or something? It's been a while since I've run an applet. Is this sandboxed somehow?
SnapKit is a huge framework with lots of functionality. One key part for the browser integration module (SnapTea) is TeaVM https://github.com/konsoletyper/teavm
TeaVM converts Java code to run in the browser. It provides the ability to call JS functions to access browser features like canvas and XHR. However, unless you want to be coding like Vanilla JS, you'll want a framework on top. SnapKit provides that.