Last week, a friend who won at pachinko treated me to yakiniku. It was all-you-can-eat and I stuffed myself.

Literal

Last-week [topic-は] pachinko [at-で] won friend [by-に] grilled-meat [obj-を] be-treated. All-you-can-eat [at-で] to-the-fill ate.

ごちそうになる is the passive-form verb for 'to be treated (to a meal),' the polite/humble complement of ごちそうする ('to treat'). The に marks the treater (agent). パチンコで勝った is a relative clause modifying 友人 — 'a friend who won at pachinko.' 食べ放題 ('all-you-can-eat') is a standardized restaurant offering in Japan — literally 'eat-freely' ending ~放題. たらふく is an adverb meaning 'to one's fill, stuffed,' with a slightly casual flavor. Polite register throughout.