It angers me that she isn't wielding a daisangen tsumo

Actually, this is not yet a closing hand. There's only 13 tiles here, whereas a closing hand requires 14. Best guess is she is declaring a riichi for Kokushi Musou.

...but one does not declare riichi with the 5000 (or was it the 10000?) stick! =))

It's probably because one of her signature moves in the game is called "Thirteen Orphans". I know nothing about Mahjong, but I'm assuming it's a reference to this hand.

It is a reference, it is of the 7 ultimate hands in mahjong. Too bad they didn't show the last three tiles clearly and Astana's right it's not a closing hand, she needs one more wind tile or dragon? tile to complete the hand.

She's got a hand set up, but it's not 13 orphans, I forget what the hand is called, though.

In any case, all of her moves are named after mahjong hands.

No one noticed the last shadowed tile she's got in her hand in the back? I'm guessing tsumo if she's already showing the hand.