Of-course Rabbi Shmueli recites Tachnun on Nittel Nacht, or more accurately:- Mincha preceding it & Schacharis following it, except of-course when it is Chanukah, which of-course it can never be, if HaLevi is referring to Russian Orthodox Nittel Nacht.
Ironically Rabbi Shmueli does not recite Tachnun on day of Shmuel HaNovi’s Johrzeit, as Shmuel Hanovi’s Zechus led to the incredible amazing Ness of Yom Yerusholayim on his very own Johrzeit.