This practice of not putting on tefillin on chol haMoed is my own minhag. I think because of the Gra, the standard practice in Eretz Yisrael is not to wear. Many years ago, on Succos or Pesach a friend of mine put on tefillin in public at the kotel, and got yelled at by (IIRC) an elderly chareidi man for his troubles. In America, in shul, people who put on tefillin do so and those who don't do not. But in Israel, perhaps in public at the kotel, and perhaps because of the prevalence of the custom such that this person never heard of an alternate custom in the matter, someone viewed it as problematic.
Rabbi Howard Jachter has a comprehensive article on the subject. Amidst it all, he states "In fact, the Zohar strongly advocates refraining from wearing Tefillin on Chol Hamoed" which might be an understatement. Read it all -- it is interesting.
It is not just the position of the Zohar, but Zohar is just echoing certain Rishonim and stating it in stronger terms.
Rabbi Jachter also writes: "In Eretz Yisrael, the ruling of the Vilna Gaon to refrain from wearing Tefillin on Chol Hamoed has been universally accepted. One who publicly dons Tefillin during Chol Hamoed in Eretz Yisrael is inviting a strong protest from his fellow worshippers." This friend of mine experienced this firsthand.
Here is Shadal, as the guest, from the beginning of Vikuach al Chochmat haKabbalah, arguing that it one is required to wear tefillin on chol haMoed; and that even if not, it is incorrect, and terrible, to say that one who does this is liable to the death penalty. He writes:
And the man became enraged and said: One who performs the commandment of his God is liable to death? Woe to the ears which hear this! And how do you speak to put deviation of the Sages of the Mishna, to place in their mouths something like this, that one who puts on tefillin on a day of the days in liable to death? And is it not that even on Shabbat and Yom Tov they did not say that it is forbidden to put on tefillin, and that one who puts them on is liable to a punishment, neither light nor stringent, but rather they only said that Shabbat and Yom Tov are not the time of tefillin, for they themselves are a sign. And how is it forbidden to put on tefillin on chol haMoed? And do we not find in the Talmud Yerushalmi (brought down in hagahot Maimoniyot) that one of the Sages commended a scribe that he write tefillin on chol haMoed for his own needs, so that he will be able to give his tefillin to another person who lost his tefillin on chol haMoed? And if one who puts on tefillin on chol haMoed is liable to death, what will be the penalty of the scribe who writes them on chol haMoed to put them on himself, in order to lend his own to another Jew so that he too will put them on on chol haMoed?I would suggest that there is indeed an opinion that there is a violation at play, not just an exemption. If we look in Yerushalmi Berachot 14b:
ר' אבהו בשם רבי אלעזר הנותן תפילין בלילה עובר בעשה. ומה טעם (שמות י) ושמרת את החוקה הזאת למועדה מימים ימימה ימים ולא לילות ימימה פרט לשבתות וימים טובים והא ר' אבהו יתיב מתני ברמשא ותפילוי עילוי מצדדין הוה וכמין פיקדון היו בידו אית דבעי מימר לא אמר אלא הנותן אבל אם היו עליו מבעוד יום מותר
Thus, Rabbi Abahu is of the opinion that there is not just exemption on Shabbos and Yom Tov, but prohibition. As he says, עובר בעשה. My own theory of Rabbi Abahu (which I also think is applicable to certain positions in Bavli which may have been misinterpreted) is that where there is a command and a derasha which restricts to a particular time, or class of people, it is not just an exemption but an issur aseh. Thus, in that same gemara, we find that Michal bat Kushit (who is Michal bat Shaul in Bavli) put on tefillin, and the Sages did not protest. But for Rabbi Abahu, who claims this violates an issur asei, the Sages did protest!
I would guess that Shadal was unfamiliar with this particular Yerushalmi, which is not, after all, in the 10th perek of Eruvin, where it might have influenced discussions of the matter more.
This does not mean that Rabbi Abahu would agree that chol haMoed has the same status as Yom Tov, in this respect. I am only arguing on the level of whether there is a violation.
An violating an issur assei is certainly not necessarily to be equating with being liable to death. This might be poetic overstatement. Of else, an mistaken overstatement.