"Especially dumpling" is a whole new clause in addition to "I like Chinese food". In this clause, the subject and verb are elided:
I like Chinese food; I especially like (Chinese) dumpling.
So it is an elided clause. As such, we can regard it as not having a phrase structure category according to a grammar. The basic hypothesis behind elision is that there is a grammatically complete utterance in the speaker's mind, from which words are deleted. The original utterance obeys the rules of grammar and can be identified as some phrasal category like "clause". The version which is actually spoken, with removed words cannot.
For instance, what part of speech is "John Mary" in the following:
Bob is going with Jennifer and John with Mary.
it doesn't have one; if we accept the elision hypothesis (which we practically must), the speaker produced "John is going with Mary", which is a clause, and condensed it to "John Mary", which we can identify with that clause, and call it an "elided clause".
Note that "dumpling" is normally countable, but here "dumpling" is uncountable. This is a little bit strange, but it will be interpreted as being similar to "I like duck".
Of course "duck" has to be treated uncountably when we are talking about food because it is short for "duck meat"; "I like ducks" cannot be used when talking about food, whereas "I like dumplings" is the normal way to state your preference for steamed or boiled dough.
"For example" patterns can also be hypothesized as being cases of elision. Consider that a sentence like:
I like Chinese food, for example: pork dumplings, won ton soup and barbecued duck.
can be viewed as a condensed version of this string of clauses:
I like Chinese food. For example, I like pork dumplings, won ton soup and barbecued duck.
For example is a kind of introductory interjection, which indicates that the following clause gives examples. The list of foods is then a compound noun which serves as the object of the elided verb "to like", where the elided subject is "I".
Isn't it an adverb? – Safira – 2013-11-07T04:12:14.313
@Safira It is an adverb which is the part of speech,but it's not a sentence constituent,right? – user48070 – 2013-11-07T04:22:56.097
Yea. That's pretty much it. You can say it I like Chinese food., but not I like especially dumpling. That means without it, especially dumpling, the sentence is just fine. – Safira – 2013-11-07T04:31:42.607
4This should say dumplings. Unless there is only one giant dumpling in the entire world and everyone eats pieces of it, dumpling in the singular doesn't make sense here ;) – WendiKidd – 2013-11-08T03:22:39.260
I especially like dumplings is the sentence that gets cropped like the above. "Especially" applies to "like" - strengthening it. – SF. – 2013-12-16T09:55:05.933
Somehow I feel that it could be parsed in more than one way. At first glance, it's easy to understand it as [I like Chinese food] and [I especially like dumplings]. However, we can see it as an apposition too: [I like [Chinese food, [especially dumplings]]. To support this argument, try fronting: Especially dumplings, I like Chinese food, and it will not sound as good as the original version. The apposition-oriented parsing can be interpreted as: [I like [Chinese food, [specifically speaking [the dumplings]]] – Damkerng T. – 2013-12-16T18:32:26.180
@user48070 The other sentence you think similar is actually not. Kindly see my answer. – Maulik V – 2013-12-18T05:34:26.410