The problem is not really related to the IDE version, rather it's related to the version of the library which comes with that IDE version.
Try this:
- Sketch > Include Library > Manage Libraries...
- Wait for download to finish.
- In the "Filter your search..." box, type "gsm".
- Click on the GSM library entry. It will show the version you have installed, which should be 1.0.6.
- Select 1.0.5 from the drop down version menu.
- Click "Install".
- Click "Close".
- Try the example sketch again.
Repeat that process until you have either found the newest version of the library that works or have gone all the way back to the oldest version without finding one that works. If the latter, then you know the problem is due to a difference elsewhere and you can go through a similar process with other variables. I believe that the arduino.org IDE (the 1.7.x versions) includes the unmodified 1.0.0 version of the library for AVR boards. If you do find a version of the GSM library that works for you then you can either just use that version or investigate what changed between the working version and the non-working version to see what needs to be fixed in order to allow you to use the latest GSM library version.