Okay, I am now at a place where I can do some testing. I am not using the Foundations version of SharePoint but am using SharePoint 2013 online. Here's what I'm doing and what I see:

• I create an MS Project file in Project 2013 SP-1.
• After saving the file, I choose File > Share, Sync with SharePoint. That creates the SharePoint site along with the Task List. The Project file is stored in the Site Assets library.
• I go to the Site Assets library for the newly created SharePoint site and ensure that versioning is set correctly.
• I exit Project and go to the task list.
• I open the task list in Project using the SharePoint option.
• Edit, save and close.
• When I view the site assets, I can see the current version.
• If I click to view the version history, I can right click on a previous version, select open in a new tab. (This is using Chrome)
• The old project file is downloaded and I can open as needed.
• If I use IE - I need to select "Save Target As" to download a copy of the file. Directly trying to open throws the error you note. I would not open the file directly - but download a copy to avoid potential issues with sync errors.