One possible answer may be from [here][1]:

> "תיכון בית תפילתי" – תבנה את בית המקדש העתידי. (השלישי) שנקרא גם 'בית תפילה'.
"אז אגמור בשיר מזמור" – בעת הגאולה אשלים את תפילת ההלל עם חנוכת המזבח."

It seems that Tefillah is an inherent part of Beit Hamikdash. If the Mikdash was simply a house of sacrifice, ending the giving of thanks with a Shir Mizmor of Tefillah would be out of place. The only way would be to sacrifice. Therefore, the composer is telling us the important role Tefillah has in the Mikdash.
 

Another answer may be simply that "בית זביחתי" isn't a name for the Mikdash.

[1]: http://www.zeevgalili.com/2013/11/18727