Дибур Хаматхиль к Бамидбар 35:21

א֣וֹ בְאֵיבָ֞ה הִכָּ֤הוּ בְיָדוֹ֙ וַיָּמֹ֔ת מֽוֹת־יוּמַ֥ת הַמַּכֶּ֖ה רֹצֵ֣חַֽ ה֑וּא גֹּאֵ֣ל הַדָּ֗ם יָמִ֛ית אֶת־הָרֹצֵ֖חַ בְּפִגְעוֹ־בֽוֹ׃

или вражда поразила его рукой, чтобы он умер; тот, кто поразит его, непременно будет предан смерти: он убийца; кровный мститель убьет убийцу, когда тот его встретит.

Yalkut Shimoni

Or if he struck him with enmity, why is it stated "by his hand"? Because it states "or if he struck him with an iron tool" etc., "or with a stone" etc., "or with a wooden tool" etc. I only know that if he killed him with those, he is liable. How do I know that if he choked him, strangled him, or kicked him, he is also liable? It is stated "by his hand" from any manner of killing.