It says that before the Jews had relations with the Midyanite women that eventually led Pinchas to kill Kozbi and Zimri they ate of their Idolatrous sacrifices and then it says and they bowed to their gods what is the addition of eating coming to tell us?
The simple reading of the verse is that they ate meat that had been slaughtered as part of the idol worship. (Elsewhere Chazal talk about dried fruit and other "high-residue" foods with regard to Ba'al Pe'or, but specifically in this verse, it sounds like it's talking about meat.)
טו פֶּן-תִּכְרֹת בְּרִית, לְיוֹשֵׁב הָאָרֶץ; וְזָנוּ אַחֲרֵי אֱלֹהֵיהֶם, וְזָבְחוּ לֵאלֹהֵיהֶם, וְקָרָא לְךָ, וְאָכַלְתָּ מִזִּבְחוֹ. טז וְלָקַחְתָּ מִבְּנֹתָיו, לְבָנֶיךָ; וְזָנוּ בְנֹתָיו, אַחֲרֵי אֱלֹהֵיהֶן, וְהִזְנוּ אֶת-בָּנֶיךָ, אַחֲרֵי אֱלֹהֵיהֶן
Watch out for the pagans, as they will stray after their idols and invite you to join them in the meat from the animals they've offered to their gods, and one thing leads to the next, your kids are married to them and worshipping idols.
וַיֵּשֶׁב יִשְׂרָאֵל, בַּשִּׁטִּים; וַיָּחֶל הָעָם, לִזְנוֹת אֶל-בְּנוֹת מוֹאָב. ב וַתִּקְרֶאןָ לָעָם, לְזִבְחֵי אֱלֹהֵיהֶן; וַיֹּאכַל הָעָם, וַיִּשְׁתַּחֲווּ לֵאלֹהֵיהֶן. ג וַיִּצָּמֶד יִשְׂרָאֵל, לְבַעַל פְּעוֹר
The people started straying towards the pagan girls; the pagan girls invited them to join in the meat slaughtered to their gods, the people ate [it], bowed to their gods, and got seriously attached to the idolatry.
Basically, everything that God warned about in Exodus, happened here. "Oh I'll just hang out with a pretty girl, her religion has nothing to do with it." "Oh I'll just have dinner with her, okay fine maybe the roast beef was involved in her ritual, but I don't believe in it ..." and before you know it, boom, idol worship.
It's a cautionary tale, explaining why boundaries were set.
The so called god they worshiped was the Baal Peor the way it is worshiped is be defecating on it. The Jews in the Desert ate Maan the perfect food which had no extra bran so they did not produce Fecal matter and did not need the Bathroom (something they complained about, this might explain the complaint and why it angered Hashem) hence the Posuk has to specify they ate of the Idolatrous sacrifices and only then where they able to Worship their "gods".וד"ק