It’s been a while since Microsoft launched Office 2013, and with Office 2016 soon coming out they still have not thought about giving Visio 2013 files a file icon in the search results.
I’ve created some files to remedy this for anyone interested. The files can be found over at https://github.com/wobba/Scripts/tree/master/VSDX-Patch
The only thing not handled is making the files appear in the Result Type refiner. If you make a copy of the filter_default.html file you can fix this yourself by adding the 2013 extension in the mapping function (Search for Visio and you will find it)
You can run this against your search center or any other site which uses osssearchresults.aspx.