You really only need a single article, and that article matches the first item in your list:
It is not a product, service, desktop application, machine, or application...
While it is true that you wouldn't say "a application" (since it starts with a vowel), by having declared the first item in the list as indefinite, the presumption of indefiniteness (a vs. the) is implied on all subsequent items in the list.
If your list were ordered differently, you'd write:
It is not an application, product, service, desktop application, or machine ...
In either case, the repetition of the article on each item is superfluous, and may safely be omitted
Note, if you mix classes of nouns - definite, indefinite, and mass quantities, you need to mark at least one of each class. For example:
Feel free to use a phone, fax, or the Internet to reach me.
It would be any old phone or fax, but since there is only one Internet, it needs the definite article.
N.B. Your sentence would read best if you say "It is not a product, service, desktop application, machine, or application, but rather an architecture." (or better yet, framework!) But saying "rather" you signal the reader to the fact that you are switching to what the thing is.