Hi Daniel,
In ArcGIS Pro, does the Import Map option on the Insert tab work?
For ArcMap, just double-clicking the map package from it's file location should work to open the map package. Is that successful at all? Keep in mind, sometime map packages take a while to open as they include data.
If not, maybe try a different map package? There's one publicly available that opened without issue for me here:
http://www.arcgis.com/home/item.html?id=865a0212b33b44adbe8a42d530c5f541
If that works, and the original doesn't, it may be a problem with the map package itself.
Best,
-Lauren