This is what I thought (more or less). So you need to obtain the fonts, put them on an intranet font server, and set up your intranet site to use the font server. (Can be the same server). This is a complex task, the Adobe web site is taking care of many details.
By the way, you seem to suggest that the fonts on the font server will be fetched by the web server. But web fonts are fetched from every separate web client. These are the ones needing access, the intranet web server does not care. Since this is unlikely to be possible you need your own intranet font server. Be sure you have a large budget for the font licensing, this is not a small detail.