This doesn't make sense to me. If it is a match, as in something to start a fire, shouldn't it be panjang? Lama means a long period of time. If it's talking about a match, as in a romantic liaison, then it's just a weird sentence....
Dear Susan, "pertandingan" is a match like a football match (or another sports match), not a match to light a fire, that would be "korek api".
"korek api mereka panjang" is correct when talking about a match to light a fire.