This is a bit tricky. When you define a custom theme, you specify variables and import bryntum's scss file. So as an output you're going to have a css built automatically for the scss provided. How can I define different scss sources in one project? The only way I see it, create css in advance, for example with sass preprocessor. Then it might work. But I cannot find a solution to integrate 2 custom theme in a build process of Vue application. That's why I wonder if you can provide a small example showing how to achieve this in Vue app.
Yep, you'll need a SASS compiler(bundler).
After you copied our theme sources and applied required changes, you'll need to compile files to CSS file, which you'll define in index.html (or similar). If you have 2 themes, put them all together using tags