It largely depends if you are tax resident or not.
It is "sort of true" that receipts are no longer needed. If you are tax resident you may be entitled to a rebate on your assessed tax, used in Greece instead of a tax free allowance, depending on your income level. Receipts were used to determine if you qualified for that tax rebate. You did not actually submit them to the tax office but you did need to declare on your tax return the total value of the receipts you had collected that year. That amount would be compared with your total income and if you had collected sufficient receipts you would be entitled to the full refund. The exact value of the refund depended on your income. For large incomes the refund reduces.
As Evansmr1 says, a few years ago the system changed so that qualification for a full rebate would be determined by the amount you spent electronically, i.e. with cards or bank transfers, standing orders and direct debits. If you are over a certain age, I think it might be 70 but don't quote me, you can still opt to use receipts if you want to. Personally I now rely on electronic payments to qualify for the rebate.
The reason I wrote "sort of true" is because of tax audits. I have had to undergo 3 tax audits in the last ten years. Each time I underwent a tax audit I had to submit the actual receipts collected for the years being audited. Exactly how many years the tax office decides to audit depends on the reason for the audit. In my case they only ever audited one year so I had to submit receipts for that year. The tax office can, if they wish, go back over a number of years; I think it is seven but I am not certain. Since going back seven years from today would include years before the new system came into effect it is possible that somebody could be asked for receipts from those years. That is why I recommended keeping them at least for now.
If you are not tax resident I am not sure if there has ever been a need to keep receipts? Even if you had some Greek income and that was assessed for tax in Greece you do not qualify for the rebate if you are not tax resident so I am not sure what purpose the receipts would serve. Non tax resident ex-pats tended to be allocated an assumed income based on things they own, like a house, a car, a swimming pool etc. They were then expected to produce pink slips to prove that they had brought at least the assumed income into the country. I am not sure if that requirement continues.
Electronic spending is monitored by the financial institutions carrying out the transactions, e.g. banks, credit card companies etc, and they inform the tax authority automatically how much you have spent in that way. On Alpha bank online banking I can see the accumulated amount and also, if I specify my income, I can see what percentage of the requirement I have achieved so far. That latter part doesn't really work for me because I use two accounts with completely unrelated banks so I need to combine the electronic spending from both.