Do non Lubavitchers believe there is a significance in getting him to put on tefilin more than a different mitzva? Say krias Shema maybe.
I didn't read the question properly and thought you were asking why tefillin is significant, and didn't realize you were asking *non Lubavitchers* and wrote this response. Even seeing my mistake, I'm posting here in case it is of interest to anyone. This could be a lengthy answer, but for starters:
A) when we put tefillin on with someone they say shema (first parsha. If they have time and/or can read, they might do all 3). And some, albeit not that common, will put on tzitzis with the person as well.
B) Yes, there is a special emphasis placed on tefilin over other mitzvahs. The Rebbe started numerous campaigns, or mivtzoim, the first was tefillin. See here for a primer:
https://www.chabad.org/therebbe/article_cdo/aid/62228/jewish/10-Point-Mitzvah-Campaign.htmC) Mivtzah tefillin was started before the 6 day war. Quoting the pasuk, וראו כל עמי הארץ כי שם ה' נקרא עליך ויראו ממך, which The braisa says is referring to tefillin shel Rosh, the Rebbe said putting on tefilin with people, especially soldiers, would strike fear into the enemy and bring yeshuah to the yidden. For a more detailed read of the history, see here:
https://derher.org/wp-content/uploads/56-Iyar-5777-06.pdfD) The Rebbe also made mention that tefillin is unique in that if a head wears tefillin even just one time it changes the person into a different category. (which is why Lubavitchers make a big deal when putting on tefilin with someone for the first time, calling them a "Karkafta", from the term "Karkafta d'lo monach tefillin.)
E) My grandfather once asked the Rebbe why tefillin (on someone else's behalf), the Rebbe gave the above reason, plus a second reason - watch the full story here:
https://www.chabad.org/therebbe/livingtorah/player_cdo/aid/3706101/jewish/The-Full-Picture.htm or read it here:
https://www.chabad.org/therebbe/article_cdo/aid/133500/jewish/Why-Tefillin.htm