The issue is two-fold: 1) I misunderstood that when using MEAN, express.js is creating a web server for me. So any special handling of content-types needs to be done within express.js configuration files and main js file. 2) I was encountering the original issue because in DigitalOcean, I am running under "production" NODE_ENV path, instead of "development". As such, my lib/node config file was looking for files in different root paths. That resulted in my index.html looking for all script files in a path that was valid for development environment, but not in production. Therefore, my app was returning "index.html" as a failover whenever an unknown path was requested, resulting in chaos.
Lesson learned, best to test multiple environments as best as possible before deploying to actual production environment.