Why Salayatana is ommitted in this mode of Dependent Origination? Why Salayatana is ommitted in this mode of Dependent Origination?

"If one is asked, 'Is there a demonstrable requisite condition for contact?' one should answer, 'There is.'

"If one is asked, 'From what requisite condition does contact come?' one should say, 'Contact comes from name-and-form as its requisite condition.'

http://www.accesstoinsight.org/tipitaka/dn/dn.15.0.than.html
I'm not sure it is omitted: it's listed there as "consciousness":


  From consciousness as a requisite condition comes name-and-form


I think that the ṣaḍāyatana are sometimes translated or understood as consciousness (which is listed in DN 15):


  More specifically, according to this analysis, the six types of consciousness are eye-consciousness (that is, consciousness based on the eye), ear-consciousness, nose-consciousness, tongue-consciousness, body-consciousness and mind-consciousness


The word used in DN 15 is viññāṇa (the following quote is also from Wikipedia's Vijñāna article):


  Hence, in this context, viññāṇa includes the following characteristics:
  
  
  viññāṇa arises as a result of the material sense bases (āyatana)
  there are six types of consciousness, each unique to one of the internal sense organs
  consciousness (viññāṇa) is separate (and arises) from mind (mano)
  here, consciousness cognizes or is aware of its specific sense base (including the mind and mind objects)
  viññāṇa is a prerequisite for the arising of craving (taṇhā)
  hence, for the vanquishing of suffering (dukkha), one should neither identify with nor attach to viññāṇa
  


I think that glossaries (e.g. here and here and here), and the so-called Viññana Sutta, say that although viññāṇa is a broad term it may include the six kinds of consciousness.

Or see this answer, which I think is saying that viññāṇa is used in two ways: technically as a specific aspect of mind, and colloquially to refer to several aggregates. 



In case you want to read more (I'm sorry to post links instead of answering the question here, but they're long), Piya Tan of dharmafarer.org (for example) has written about this at some length.

Here is his analysis and translation of DN 15. The introduction starts with,


  Moreover, its series of conditions omits three factors of the standard version: ignorance,
  volitional activities [saṅkhāra], and the 6 sense-bases. These omissions have led some
  scholars to suggest that the twelvefold formulation may be later augmentation of a shorter original;
  but such suggestions remain purely conjectural, misleading, and objectionable on doctrinal
  and textual grounds. All in all, omissions of the Mahānidāna Sutta are more than compensated
  for by its detailed explanations, interesting digressions, and supplementary sections.


And on page 156 (page 12 of the PDF):


  In the next section of the sutta, instead of going on to the 6 senses
  and their respective contacts, as in the standard formula, the Buddha reverses his last statement and
  says: “With name-and-form, there is consciousness”. To prevent any misunderstanding, the
  Buddha then, introduces a remarkable passage unique to this Sutta: etc.


It doesn't seem to bother him that this sutta uses an other or a non-standard description. I don't know "why" it is slightly different but I find that unremarkable. It seems to me like asking, "Why is the house described as 'brown' here, whereas there it's described as 'made of stone'? Are they two different houses?" They're two descriptions of the same house.

Furthermore, here is Piya Tan's essay on the meaning and usage of vinnana (which I won't quote).

I'm not sure that it's necessary to put "6 sense bases" as a distinct layer between form and contact -- for example I think it makes as much sense to say that there are 6 types of contact.

For what it's worth, the 6 sense-spheres are omitted from the description of the five aggregates too.