If you check other sources as well, it seems to, in fact, be 1000 times gravity. For example check The Audubon Society where it's quoted as '1500 g-force' units, compared to about 5 on a rollercoaster, this paper which seems to show it as even greater in figure 2 or The Zooilogical Society of London which cites 10000 m/s/s or around 1000 g.

Interestingly, as woodpecker brains apparently weight about 2.5 grams, the difference between 9.8N of force and 1000 g=0.0025*9.81*1000=24.525N isn't all that great. From reading around it seems their skulls and tongues don't even absorb much impact. as it'd make their digging less efficient, their brains are just light enough and structured so they don't get damaged.