I'm following the same tutorial you are, using a Jupyter notebook with the Python API, and getting the same issue you are: an HTML file that shows up as a blank webpage when I try to view it in a web browser by opening the file locally.
This is the code I'm using as a minimal working example:
from arcgis.gis import GIS
gis = GIS()
map2 = gis.map()
map2.export_to_html('test_map.html')
The resulting HTML file cannot be attached in a comment on this forum, but you can see it here: ( http://erinkiley.com/test_map.html ) and can read what's in it by choosing "view source", however your particular browser lets you do that. Point is, the file's not blank (far from it: it contains some 13k lines).
The comment I linked from 2014 in the Javascript API forum is related to the same issue: a user exported a map to an HTML file (using the Javascript API---yes, it's different from the Python API, but hear me out), and the exported HTML file showed up as a blank webpage when the user tried to view it in a web browser by opening the file locally. The comment on that post reads, in its entirety, "just to be clear. You HAVE to run the file on a server. You cannot run it locally (file://)".
I am really not a web developer, just looking to generate a map I can share with my boss. I don't know if there's such a thing as an HTML file that cannot be viewed when it is "run locally", but that can be viewed when it is "run on a server". But it seems like the behavior I'm seeing---both from the example I've tried, from the example you've tried, and from the example on the Javascript API forum (especially with that comment, cryptic as I think it seems)---is consistent with that hypothesis.
I'm not really clear on what it means to "run the file on a server"? But I have a personal website and I placed this file on the server that provides web hosting (and changed its permissions to 755). When I try to load this file by opening my web browser (for good measure, I've tried Opera, Firefox, and Edge) and navigating to the publicly viewable URL I saved the file under, it still shows a blank page with the title "Exported ArcGIS Map Widget", just like it does when I "run it locally".
Sorry, but I'm still at a complete loss as to why this is happening with the simplest test example. Here's hoping someone with more wisdom can chime in and drop a lead for us to follow.