You don’t have to be Romanian resident. But you have to go to the bank in person. With a passport preferably (with national IDs is a bit more complicated )
The free ATM promo seems to be temporary but always extended. Heard about someone using the card for few years already.
Btw. Most Romanian banks open accounts even for non EEA residents as long as you deposit money. I have a Lebanese friend who opened an account last summer using a schengen tourist visa