Why do we need special key-wrap algorithms? Wikipedia says:


  Key Wrap constructions are a class of symmetric encryption algorithms designed to
  encapsulate (encrypt) cryptographic key material.


We are using these algorithms to encrypt (and authenticate) a key, using a symmetric algorithm (and symmetric key, named key encryption key).

Some of these algorithms are quite complicated, like the AES-keywrapping algorithm AESKW defined by NIST originally in 2001, with a new draft 800-38F available now. In the following image, each red box is one invocation of the AES block cipher, to encrypt in total only 256 bits (i.e. 2 blocks) of plaintext (including a constant part as integrity check/authentication):

(Image from Figure 7 of Deterministic Authenticated-Encryption - A Provable-Security Treatment of the Key-Wrap Problem, by Rogaway/Shrimpton, 2007.)

Why do we need such complicated algorithms, when a simple combination of CBC or CTR mode with a MAC, or an authenticated encryption mode like AEX would give us the same security result?
The paper you cite (Deterministic Authenticated-Encryption...) gives quite a bit of useful information (but I'm assuming you already knew that). It looks like a pretty good read (I'll let you know if that assumption holds after I finish it).

For why simpler constructions (CBC/CTR with a MAC or even AEX mode) don't satisfy (emphasis added):


  A key-wrap scheme is a kind of shared-key encryption scheme. It aims to provide “privacy and integrity protection for specialized data such as cryptographic keys, . . . without the use of nonces” (meaning counters or random bits). So key-wrap’s raison d’etre is to remove AE’s reliance on a nonce or random bits.


The reason for removing the nonce/IV/random bits, at least according to the paper, is to make the protocol "more resilient to IV misuse."

I also found the following paragraph useful (emphasis added):


  That said, in many contexts where one would think to use key wrap, one can use a conventional AE scheme, instead. This does not make studying the key-wrap problem pointless. First, it clariﬁes the relationship between key wrap and conventional AE. Second, DAE leads to misuse-resistant AE, and methods that achieve this aim make practical alternatives to conventional (not misuse-resistant) two-pass AE methods. Finally, practitioners have already “voted” for key-wrap by way of protocol-design and standardization efforts, and it is simply not productive to say “use a conventional AE scheme” after this option has been rejected.


Another potential reason for key-wrap algorithms is their analyzability. I'm not completely sure about this, but it could be that under the key-wrap algorithms, security is provable, but that might not be possible under a more simplistic approach.

On a side note, when reading through the intro to that paper, it made me wonder how the notion of Entropic Security plays into key-wrap algorithms. In the paper, they briefly mention it as a related work, but that is all.