These files are intended to be used with Import-PSTypeExtension. Save the file locally and run the import command. You must specify the full file name with file extension, so the function knows how to import the data. Importing will overwrite any existing type members with the same name. The new type members will only last for the duration of your PowerShell session. If you always want a set of type extensions, put the Import-PSTypeExtension command into your PowerShell profile script.
Get-ChildItem c:\scripts\myextensions\*.json | Import-PSTypeExtensionImport ps1xml files into your session using Update-TypeData. You may see error messages about existing type extensions. When importing a .ps1xml file there don't not appear to be a way to force overwriting existing extensions. But any new extensions will be loaded into your session.