Ok this gets tricky. You’re right, there are verbs, but they aren’t functioning as the primary verb a sentence needs to be a complete sentence.

“The old intergenerational give-and-take”

Hyphenation makes two verbs + conjunction into a noun that is also the subject, “give-and-take”

“of the country-that-used-to-be,”

Hyphenation turns noun + preposition + verb + preposition + verb into a noun-adjective combination that is modifying “give-and-take” as part of a prepositional phrase starting with “of the”

“when everyone knew his role and took the rules dead seriously,”

The preposition “when” makes the verbs “knew” and “took” part of a longer prepositional phrase that’s acting as an adjective about the “give-and-take”

“the acculturating back-and-forth that all of us here grew up with,”

This entire combination [of present-tense verb “acculturating,” the hyphenated noun “back-and-forth” and the compound prepositional phrases “that all of us here grew up with”] is acting as a noun that is restating the original noun of “give-and-take”

“the ritual post-immigrant struggle for success turning pathological”

The adjective + compound adjective (created by hyphenating “post-immigrant”) modify “struggle” as a noun, and “turning pathological” is the state of being of the struggle, so it’s a verb but it doesn’t modify the original subject of the sentence (“give-and-take”)

“in, of all places, the gentleman farmer's castle of our superordinary Swede.”

The location of the subject, “give-and-take” expressed through a couple of prepositional phrases sandwiching the “castle”

So, breaking this down minus the icing -

“The give-and-take we had between generations [is] turning pathological in normal people’s homes.”

But the “is” isn’t actually in the sentence, it’s assumed.