(יב) אַשְׁרֵ֣י הַ֭גּוֹי אֲשֶׁר־יְהֹוָ֣ה אֱלֹהָ֑יו הָעָ֓ם ׀ בָּחַ֖ר לְנַחֲלָ֣ה לֽוֹ׃
(12) Happy the nation whose God is the LORD, the people He has chosen to be His heritage.
I think the verb "choose" is said in reference to the noun "heritage" in Shabbos Shacharis too.
The beracha's agenda is to draw a pointed contrast between the groups/nations who Hashem didn't give the Shabbos with the group/nation that Hashem did give the Shabbos to, in terms of how he gave it over and to which group He gave it to.
Based on this, although it isn't explicit in the beracha, the corresponding clause of
וְלא הִנְחַלְתּו מַלְכֵּנוּ לְעובְדֵי פְסִילִים...is לְזֶרַע יַעֲקב אֲשֶׁר בָּם בָּחָרְתָּ. To illustate better:
Based on this, although it isn't explicit in the beracha, the corresponding clause of
וְלא הִנְחַלְתּו מַלְכֵּנוּ לְעובְדֵי פְסִילִים...is לְזֶרַע יַעֲקב אֲשֶׁר בָּם בָּחָרְתָּ. To illustate better:
וְלא נְתַתּו ה' אֱלהֵינוּ לְגויֵי הָאֲרָצות.
וְלא הִנְחַלְתּו מַלְכֵּנוּ לְעובְדֵי פְסִילִים...
כִּי לְיִשרָאֵל עַמְּךָ נְתַתּו בְּאַהֲבָה.
לְזֶרַע יַעֲקב אֲשֶׁר בָּם בָּחָרְתָּ:
You did not give it, Hashem our G-d, to the nations of the lands,
Nor did you make it an inheritance to the worshippers of idols...
For to Israel, your people have you given it in love,
to the seed of Jacob who You have chosen.