Only the receipts purchased within the relevant 2 months qualify.
The new short receipts are also eligible. However, this was my most recent experience with the new short receipts:
I went into a 7-11 to redeem my winning ticket from May-June by purchasing $200 worth of items. In the past, there were no problems with the long reciepts--simply print my info on the back, including my ARC number.
However, the clerk informed me that with the new short tickets, the clerk MUST scan the barcode on a Taiwanese ID to enter the winner's information into the system. Although ARCs have a barcode, apparently they don't contain the information that is required (the manager of the 7-11 confirmed this). So, the clerk ended up using his own ID to process my transaction.
So, if you're redeeming a short receipt to purchase items/add to an icash card, instead of getting cash at the post office, it's more of a hassle.
If someone else has had a different experience (which wouldn't surprise me), I'd love to hear it.