Do I need a website to use XPay?

No. There is the Pay-by-Link integration mode, which allows you to send payment links to customers without the need to necessarily have a website. https://developer.nexigroup.com/xpaygreece/en-EU/docs/pay-by-link/

You can also perform MOTO (Mobile Order / Telephone Order) transactions via back office or via API, according to your contract.