No, you do not need a Square Enix Members account to purchase from the Square Enix Store as a guest checkout is available.
However, we strongly recommend that you create an account or log into your account before placing an order as the details will be stored and you will be able to keep track of this information. This functionality is unavailable when using the guest checkout, and any detailed information on your order will need to be requested by clicking on the Store Support button in the top right-hand corner of this page.
Please also note that you will not acquire any Reward Points if you make a purchase and are not logged into a Square Enix Members account.