Upgrading my project to latest MonoGame 3.6 runtime solved the issue.
Here is how I did it, since I had trouble with just replacing the referenced libraries and using my old .xnb resource files.
- get latest installer for Visual Studio
- create new "cross platform desktop" project from MonoGame templates
- add all my .cs files, add all content files to the Pipeline tool config file
- fix an issue with LoadContent() function being called each time graphics.ApplyChanges() is called
- run the project
Could not update the reference through NuGet package manager, because I was still missing the SDL2.dll. Once I got this, it started complaining about soft_oal.dll. Once I got this, it started complaining about yet another dll... Never ending story - figured out that the template should have all the proper DLL files in it and that it will be easier to setup a project from scratch. It worked.