You do not have enough self-closing / at the end of your code. Perhaps the browser does not fix this for you.
<link rel="stylesheet" href="/node_modules/angular2-busy/build/style/busy.css" />
Also, removing rel = "stylesheet" will definitely not fix the problem, since the browser needs to know exactly which link you are accessing.
If the closing tag fix does not work, your path is wrong. You can also try adding ../ to the beginning of your journey. This will make it relative to the folder in which the site is located.
<link rel="stylesheet" href="../node_modules/angular2-busy/build/style/busy.css" />
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