Radak: Beis ha'Melech was near Beis Hashem. The wall was between them. When Shlomo built his house, it says "v'Olaso Asher Ya'aleh Beis Hashem" (Melachim I, 10:5). It says about Yo'ash "va'Yored Es ha'Melech mi'Beis Hashem va'Yavo'u b'Soch Sha'ar ha'Elyon Beis ha'Melech" (Divrei ha'Yamim II, 23:20).

Malbim: Until now, the kings' houses were near Beis Hashem. The Saf of their houses was near Saf of My house. Only the wall of the Mikdash separated between Me and them. Via this, they were Metamei My Kadosh name via their abominations. Sin and Tum'ah are according to the Kedushah of the place. A light Tum'ah that is not Metamei in a Chulin place, it is Metamei in a Kadosh place. We find that a Shelishi l'Tum'ah (it touched a Sheni, which touched a Rishon, which touched an Av (source of) ha'Tum'ah, it is Metamei Terumah, and a Revi'i is Metamei Kodshim, even though they are not Metamei Chulin. So a small sin done close to the Mikdash blemishes. Therefore, He will distance Zarim from the Mikdash; Kohanim and Leviyim will dwell around it. So it was in the Midbar ? Leviyim camped around the Mishkan, "veha'Zar ha'Karev Yumas" (Bamidbar 1:51).

Radak: The matter is repeated in different words, like is common, for Mezuzah is the Saf (side of the opening).

Radak citing Targum Yonasan: They put their Saf opposite the Saf of My Beis ha'Mikdash, and their buildings by My Azarah and the wall of My Beis ha'Mikdash between My word and them.

Rashi: This is like v'Achaleh ? I will eradicate. Radak ? the last letter of the root (Hei) is omitted.