Is this the quickest way to clearing the board to two kings? Is 21 moves the least needed to get board down to 2 kings? 

[FEN ""] 
1. e4 d5 exd5 Qxd5 Qh5 Qxa2 Qxh7 Qxa1 Qxh8 Qxb1 Qxg8 Qxb2 Qxg7 Qxc2 Qxf8 Kd7 Qxf7 Qxc1 Ke2 Qxd2 Kf3 Qxf2 Ke4 Qxf1 Qxe7 Kc6 Qxc7 Kb5 Qxc8 Qxg1 Qxb8 Qxh1 Qxa8 Qxh2 Qxa7 Qxg2 Kd4 Qd5 Kxd5 b6 Qxb6 Kxb6
Samuel Loyd found faster in 1895.

[FEN ""]
1. c4 d5 2. cxd5 Qxd5 3. Qc2 Qxg2 4. Qxc7 Qxg1 5. Qxb7 Qxh2 6. Qxb8 Qe5 7. Qxc8+ Rxc8 8. Rxh7 Qxb2 9. Rxh8 Qxa2 10. Rxg8 Qxd2+ 11. Kxd2 Rxc1 12. Rxg7 Rxb1 13. Rxf7 Rxf1 14. Rxf8+ Kxf8 15. Rxa7 Rxf2 16. Rxe7 Rxe2+ 17. Kxe2 Kxe7


https://pdb.dieschwalbe.de/search.jsp?expression=PROBID=%27P0001931%27

This is 17.0 moves.

It is also possible to do it in 16.5 moves but I can't find it yet. See François Labelle's page.