If the same position — the same pieces on the same squares, the same pieces in hand, the same player to move — appears for the fourth time, the game ends in a draw by repetition, sennichite 千日手.
In professional shogi a sennichite game is replayed immediately with colours reversed. On this site it is recorded as a draw.
The exception: perpetual check
If one player gave check on every one of their moves during the repetition, that is perpetual check, and it is not a draw — the player giving the checks loses.
That rule exists because otherwise a losing player could hold a draw forever just by checking. So in shogi, if you're checking and the position is repeating, you must find something else to do.
The site applies the conservative reading: it only calls perpetual check when every move by one side, from the first time the position appeared, was a check. Anything less is an ordinary draw.
Try it
Try it: Give check with the rook along the back rank.