Why is this the inverse of a Enigma Machine rotor?
The example is using a shorthand notation for the rotors that somewhat obscures the way they actually work.  For example, the first rotor in your example, BDFHJLCPRTXVZNYEIWGAKMUSQO, actually applies the following permutation of the alphabet:

ABCDEFGHIJKLMNOPQRSTUVWXYZ
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
BDFHJLCPRTXVZNYEIWGAKMUSQO


Applying this rotor in the reverse direction thus, obviously, gives the inverse permutation:

BDFHJLCPRTXVZNYEIWGAKMUSQO
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
ABCDEFGHIJKLMNOPQRSTUVWXYZ


Now, the same inverse permutation can also be written equivalently as:

ABCDEFGHIJKLMNOPQRSTUVWXYZ
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
TAGBPCSDQEUFVNZHYIXJWLRKOM


You can check that these are, indeed, the same permutation: both map A &rarr; T, B &rarr; A, C &rarr; G, and so on.  The only difference is the order in which the individual input/ouput letter pairs are listed: in the first version, they are sorted by the output letter, while in the second version they are sorted by the input letter.

Now, the page you're reading is using a shorthand notation where the permutations are always sorted by the input letter, and only the output letters are actually shown.  This gives a nice and compact notation, but it does make it a bit harder to e.g. see whether two permutations are actually inverses of each other.