This might not be relevant - but are you sure that the specific version of Visual Studio you're using has support for SSIS projects?

Just to eliminate this....using the same version of VS that you're using to try to open this package.....try to create a new empty SSIS project. If you don't see SSIS as a project option, then it means you've got VS installed but not the database/BI project templates (for SSIS, SSAS, SSRS). And that would be the answer.

If that doesn't answer it, let me know.