Windows Server 2016 no longer has an option to enable Desktop Experience from Server Manager. Instead, most (but not all) features are enabled by default. One such feature is Windows Photo Viewer, which no longer seems to be available, and there's no clear way of enabling or installing it. Luckily, there's a workaround to get it enabled again.
First of, you need to check on Server 2016 whether the required files are already present. If you have selected to install the full UI, the required files should already be there:
They should already be present on a fresh install of Server 2016, but if not, then you will have to copy the above folders and their contents from a Windows 10 x64 computer. Place the folders as stated above.
Next up, download the registry files attached to this post. This will add the required settings to use Photo Viewer to open images. For each extension, there's a separate file, so you can choose yourself which file types to open with Photo Viewer.
Note that additional file types can be added by opening one of the registry files and performing a search/replace on the extension (for example, replace "jpg" with "bmp").