。
She was reading the magazine, completely absorbed.
Literal
She [topic-は] that magazine [object-を] absorbed becoming-て was-reading.
夢中になって ('becoming engrossed,' te-form of 夢中になる) attaches as a manner adverbial to 読んでいた — 'was reading [in the manner of] becoming engrossed.' 夢中 (lit. 'middle of a dream') captures absorbed, single-minded focus, the kind that blocks out time and surroundings. The structure ~になって + [verb] productively pairs a state-change with an action: 必死になって走る ('run desperately'), 夢中になって読む ('read engrossed').