Since the leaflet-gl-vector-layer software is one of the components of the atmosphere virtual lab, this question is definitely not out of scope for this forum.
The leaflet-gl-vector-layer is actually a pure javascript leaflet plugin. It runs in the browser (not on the server). You can npm install it to use it in your own webclient applications.
The main challenge for viewing this data in the browser is actually getting the data available in your browser as well. This requires some interface with a server or your local file system. For the Atmosphere Virtual Lab the data is provided via jupyter kernels and to make this interface efficient (using a compact binary data transfer from server to browser) we developed the ipyleaflet-gl-vector-layer-plugin. So, if you want to use leaflet-gl-vector-layer without the jupyter part, you will have to find your own way of transferring the data in a compact form (for instance using opendap+jsdap, or a javascript hdf5 reader if your data is local).