As GameMaker Studio does not have regular expression functionality yet, it is rather hard to do complex checks. Existing Regular expression Extensions are also usually not cross platform.
This is a GML script to validate if a string is formatted as an email address, this will not check any MX records, it will just provide a small validation client-side to enhance your game's user experience. It works cross-platform.
Remember to also do appropriate checks on your server if you submit the data online.
Use it freely for non-commercial and commercial games as well, no attribution required.