We find that Sinai shook ("va'Yecherad Kol ha'Har" - Shemos 19:18), but we do not find that other mountains shook!
Radak (4): Even though it is not written, other mountains, such as Se'ir and Paran, shook.
Radak(4,5): This is a parable for war 1 , like "Min ha'Shamayim Nilchamu" (verse 20). Zeh Sinai - just like Har Sinai shook due to Hashem, also the entire world - "Namogu Kol Yoshvei Kena'an" (Shemos 15:15). Sichon and Og are called mountains, because they are far and very tall.
I.e. 'Harim' are great nations.
What is the meaning of "Zeh Sinai"?
Radak (4): Just like Har Sinai shook due to Hashem, also the entire world.
Malbim: [The mountains melted] due to Hashem, Who came from Har Sinai.