Microsoft no longer updates the version of Skype for Linux with new features (because they put all the new features in the Windows version because they want you to install Windows), and as that is a reasonably recently implemented feature the Skype version for Linux does not support it.
So your best bet is to either:
1. Click the link it provides you in the first message in order to view the image online.
2. Use the web version of Skype.
3. Get the other person to send it as just regular file (if there is no option to do so either get them to change the extension to something which won't be recognized as an image or get them to convert the image contents to hex or something and just shove that in a txt file so that when you receive it you can convert it back to an image and view it - it will all depend on how Skype determines on whether or not it is an image).
4. Use WINE or PlayOnLinux to run the latest version of Skype (I tried this before and could never get this to work though - if you do it with WINE it doesn't have the necessary fonts, and if you do it with PoL, the installer just fails).
5. Switch from Skype to a different program which does still properly support Linux (personally I would highly recommend that you switch to Tox which is a great new privacy focused program with many different clients for many different devices. You can install Tox (I would personally recommend qTox (GUI) or Toxic (CLI) as they are great clients) by following the appropriate instructions for your OS here).
But I don't think there's much else you can do about it other than install Windows and view it in the latest version of Skype there (queue "BOO")...