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We played chess less to enjoy the game and more just to kill time.
Literal
We [topic-は] game [object-を] enjoy for-the-sake-of [rather-というより] just time [object-を] kill for-the-sake-of chess [object-を] did.
A subtle comparative phrasing. ためというより ('rather than for the sake of') sets up an A-over-B comparison for motives. ただ ('just, merely') modifies the second motive. 暇をつぶす ('to kill time') is a set expression — literally 'to crush/waste leisure.' The sentence reveals the true motive was passing time, not enjoyment.