Every number doesn't have its own name. If you observe closely there is a pattern. From 21 to 99, you can observe that every digit at tens place decides the suffix and the digit at ones place decides the prefix.
Further, the author says "because of a lot of irregular pronunciation, you have to memorize 100 different words as if it were a centesimal system". But I could say the same for English. We won't say "three-ty-three", we say "thirty-three". Hindi's irregularities are pretty much at the same level.
No, for English the thirty series is always "thirty-foo", and numbers ending in three are always "foo-three". It is true that you don't use the same word for the number when it's in the tens place (like Chinese), but that's as complex as it gets (and the teens, of course).
In Hindi 40 and 41 use a different word for 40. 51 and 53 use a different word for 50. 55 and 45 use a different word for 5. Plus there are smaller but still significant differences between pretty much every number -- e.g. it's chauBees, but puchees and chauNtees.