What are the Moshlim saying here?
Rashi and Ramban: They are saying that, after Sichon captured Cheshbon and made it his capital, he went on to capture Or of Mo'av (as well as Arnon and all the high places in that vicinity 1 and their inhabitants - Ramban). 2
Bava Basra 78b: Refer to 21:28:3:2 3. "Ki Eish Yatz'ah me'Cheshbos ... " - 'Because a fire will come out from those who calculate and consume those who do not; "Lehavah mi'Kiryas Sichon" - 'and a flame from the city of Tzadikim - who are called 'Sichin' (trees)'; 3 "Achlah Or Mo'av" - 'It will consume the one who follows his Yeitzer ha'Ra, like this donkey (Ayar) who follows pleasant talk'; "Ba'alei Bamos Arnon" - 'This refers to the conceited - as Mar said; "Whoever is coneited will fall into Gehinom!" '
All of which became permitted for Yisrael to capture.
Ramban: In fact, they also captured parts of Amon - "from the River Arnon up to the River Yabok", as the Pasuk states in Shoftim, 11:13. See also Yehoshua, 13:24-25 (and the Haftarah of Chukas, Pasuk 22).
Torah Temimah:As the Pasuk writes in Tehilim, 92:13 "Tzadik ka'Tamar Yifrach".
What are the fire and flames referring to?
Seforno, Da'as Zekenim and Hadar Zekenim: They refer to the army and strength of Sichon (the captains of his army - Seforno on Pasuk 30).
Targum Yonasan: They refer to the strong words that the 'Ba'alei Cheshbon emit and the great merits of those who read and speak Torah which consume the fire of their enemies such as those who sacrifice on the Bamos of Nachalei Arnon. 1
What is the significance of "Ba'alei Bamos Arnon"?
Ramban: The Torah is telling us that Sichon captured from Mo'av as far as Arnon, including the high places and their inhabitants.
Targum Yonasan: Refer to 21:28:2:2.
What is the meaning of "Achlah Ar Mo'av"?
Da'as Zekenim and Hadar Zekenim: Sichon ravaged Mo'av; so was done to him (via Yisrael). 1
Bava Basra 78b: This to one who follows his Yetzer ha'Ra, like an Ayar (donkey) follows a nice Sichah. (Fire consumes him.) Ba'alei Bamos Arnon are haughty people, who fall to Gehinom.
Targum Yonasan: Refer to 21:28:2:3*.
Targum Yonasan goes on to explain the next Pasuk in connection with the people of Mo'av who hate the Tzadikim. It is difficult to understand his connection between Mo'av on the one hand, and Torah and Tzadikim on the other.
