Even those that require you give a certain amount of "notice" before you quit your current job (two_week notice is standard) often may not provide any formal requirement that you do so by writing a letter of resignation or explain in detail why you're leaving.
Why a Resignation Letter? In these digital times, why should we submit a resignation letter, anyway? A paper trail does seem old_fashioned, but in this case, it's a best practice. It makes your intentions clear, as well as the conditions. You're removing any ambiguity about the end of your time there.