Not quite. 2^63 is 9223372036854775808, and the max value for a signed 64-bit int would be one less than that. Close enough to wager that the article may have been slightly off.
Yep, the figure mentioned is 2^63 cents, rounded to the nearest hundred dollars. I'd wager the article rounded, though I'm not sure why.
EDIT: gus_massa's theory makes a lot more sense, especially considering that the guy said he donated 30 bucks, and then afterwards his account listed $0. Presumably he had 2^63 cents + 30ish dollars, which was rounded up.
Probably the last two digits are used for cents (like in a Decimal type) and perhaps he has $41,92 real dollar in his account (or the reporters just decided to round it).