True, the performance of all the mitzvos have the potential to bring redemption, but
how much more so does this apply with regard to increasing in the observance of the mitzvah of kindling Chanukah lights,וְעַל אַחַת כַּמָּה וְכַמָּה עַל יְדֵי הַהוֹסָפָה בְּקִיּוּם מִצְוַת נֵר חֲנֻכָּה,
i.e., not only to perform the mitzvah, but to increase its observance. This is accomplished either by encouraging others to kindle Chanukah lights, or by performing the mitzvah with extra hiddur that enhances its observance.
For this mitzvah has a unique connection to the ultimate deliverance and salvationשֶׁמִּצְוָה זוֹ שַׁיֶּכֶת בִּמְיֻחָד לְהַיְשׁוּעָה וְהַהַצָּלָה,
the Future Redemption to be brought about by Mashiach,הַגְּאֻלָּה שֶׁתִּהְיֶה עַל יְדֵי מָשִׁיחַ,
since Mashiach – and also Eliyahu, the herald of the Redemption1 – are among the eight “princes of men.”מִכֵּיוָן שֶׁמָּשִׁיחַ, וְכֵן אֵלִיָּהוּ מְבַשֵּׂר הַגְּאֻלָּה, הֵם מֵהַשְּׁמוֹנָה נְסִיכֵי אָדָם,
Scripture2 and our Sages3 speak of seven shepherds of the Jewish people and eight “princes of men.” Mashiach and Eliyahu are included in the latter grouping.
They correspond to the eight Chanukah lights.4עִנְיַן שְׁמוֹנָה נֵרוֹת דַּחֲנֻכָּה.
There is another unique dimension of the connection between the Chanukah lights and the Future Redemption.וְעוֹד עִנְיָן בְּהַשַּׁיָּכוּת הַמְּיֻחֶדֶת דְּנֵרוֹת חֲנֻכָּה לַגְּאֻלָּה הָעֲתִידָה,
Just as the Chanukah lights will never be nullified,5דִּכְמוֹ שֶׁנֵּרוֹת חֲנֻכָּה אֵין בְּטֵלִין לְעוֹלָם,
so too, the Future Redemption will be an eternal redemption, whose nature is such that it is not possible that there be an exile afterwards,6כֵּן גַּם גְּאֻלָּה הָעֲתִידָה תִּהְיֶה גְּאֻלָּה נִצְחִית שֶׁאֵין שַׁיָּךְ שֶׁיִּהְיֶה אַחֲרֶיהָ גָּלוּת,
i.e., not only in actual fact will there not be an exile after the Future Redemption, the redemption itself is of a nature that precludes the possibility of a subsequent exile, because in that era, it will be revealed how all existence is G‑dly.
Similarly, the Third Beis HaMikdash will be an eternal structure7 that will never be nullified.וְכֵן בֵּית הַמִּקְדָּשׁ הַשְּׁלִישִׁי הוּא בַּיִת נִצְחִי שֶׁאֵינוֹ בָּטֵל לְעוֹלָם,
As will be realized with the coming of our righteous Mashiach, may he come and redeem us and lead us upright to our land in the immediate future.בְּבִיאַת מְשִׁיחַ צִדְקֵנוּ, יָבוֹא וְיִגְאָלֵנוּ וְיוֹלִיכֵנוּ קוֹמְמִיּוּת לְאַרְצֵנוּ, וּבְקָרוֹב מַמָּשׁ.

Summary

The performance of all the mitzvos have the potential to bring redemption, but the Chanukah lights have a unique potential to do so, because Chanukah is intrinsically connected to the Future Redemption.