As to the answer to this question, it depends what you mean by a special right really.
I, personally, do not believe that marriage is a "right"...not in the sense that its viewed today, with some kind of government sponsored benefit status. However, what I personally believe is rather useless in this context. The courts have ruled it a right and until such time as that's over turned its the basis for which we need to work.
If its a Right, then said right needs to be equally protected per the EPC clause of the 14th amendment.
Currently, there is a legitimate argument based on gender that the discrimination currently being employed by the government...wherein men can marry women but women can't marry women and vise versa...does not show that such discrimination serves an "important" state interest that "substantially" requires said discrimination to properly perform as would be required for a "Middle-Tier Scrutiny" situation.
As such, it is an equal protection issue based on gender under the 14th amendment that I believe is currently unconstitutional.
Now, with that said...more often then not when people reference EPC its with regards to discrimination against sexual preference, not gender. Sexual preference, currently, is at the minimum tier level of scrutiny and I believe there's enough there to meet that level of scrutiny. As such, until such a time that precedent happens that sets sexual preference as a middle or strict level of scrutiny, I would have to say it doesn't fall under EPC when using that argument. However, there is always the chance that if challenged in that way it may cause the court to evaluate what level of scrutiny such needs to fall under.
As I have said in a number of threads, the best option that is realistic (realizing that the government is never going to fully get out of the marriage business) is to abolish the term "marriage" from the law books and replace it with "civil union" country wide. Allow marriage to firmly and completely fall only within one realm, the private realm, rather than straddling both private and public with duel meanings and thus issues revolving around both.