I didn't actually manage to download the ciphertext you linked to — I'm pretty sure I clicked the real download button, and not the fake one in the ad next to it, but all I got was a long delay followed by an error message, and the site itself looked shady enough that I didn't feel like investigating further. However, since what you really seem to be asking is a general question about exploiting non-randomness in a one-time pad, and since anything else would be off-topic here anyway, let me just try to give a general answer.
A proper one-time pad, as the term is usually used in cryptography, requires each key letter (or byte, or whatever your cipher alphabet consists of) to be chosen independently and uniformly at random from the full cipher alphabet. As a consequence, it follows that the ciphertext will also look like a perfectly random sequence of letters.
While such a random sequence can, just by chance, contain occasional substrings that look like English words, they shouldn't appear significantly more often than any other substrings of the same length. (However, do note that the human brain tends to be good at picking apparent patterns out of randomness, so unless the non-randomness is really obvious, you really should check this with a proper statistical test rather than relying on just your intuition.)
If the ciphertext looks recognizably non-random, it's possible that either:
- the key used to encrypt it isn't really random, but might instead e.g. be the contents of some non-random file; or
- the encryption process itself might be somehow broken, e.g. some parts of the plaintext might not be encrypted at all for some reason.
In the first case, your situation is basically the same as if you were attacking a two-time pad (i.e. a proper one-time pad with a reused key). Specifically, with a reused key, combining the messages lets you cancel out the key, after which you're left with the XOR (or modular sum or difference, depending on which kind of OTP is involved) of the two non-random plaintexts.
If you're lucky, you may be able to identify the source of one of the plaintexts (e.g. it might be available online), which will then let you directly decrypt the other.
If you're not so lucky, you may be faced with a painstaking letter-by-letter reconstruction process, using crib dragging, intuition and lucky guesses to construct two plausible messages that, when XORed, yield the known XOR of the ciphertexts (or, in your case, the ciphertext itself). While this process can be automated to some extent, in my experience it tends to work poorly without close human guidance, at least unless you have a very good predictive statistical model available for at least one and preferably both of the messages.
Anyway, since this was given as an exercise, I assume it probably is solvable somehow using a reasonable amount of effort. You'll just first have to figure out exactly what's gone wrong with the encryption, to produce such a non-random ciphertext.
Ps. See also:
There are probably other relevant earlier questions on this site, too, but those happened to be ones that I'd answered myself before.