Whoever takes it first wins.

Since 1992=( 1+4)*398+2, the first picker takes two buttons first, then the second picker takes 1 2 3 4 buttons at a time, and the first picker takes 1 2 3 4 buttons accordingly. In this way, until there are only five buttons left on the table, and then the next taker takes 1 2 3 4, the remaining 4 3 2 1 is just taken away by the first taker, so the first taker always wins.