But I think you are talking about the technical sense of Khilaafah. That Khilaafah ended within 30 years of the death of the Prophet صلى الله عليه وسلم who said:
Explaining this Hadeeth, Imaam an-Nawawi رحمة الله عليه in his Sharh of Saheeh Muslim says:
قال العلامة النووي في - شرح مسلم - ج 21 ص 201 :
(( قوله ( صلى الله عليه وسلم ) ( أن هذا الأمر لا ينقضي حتى يمضي فيهم اثنا عشر خليفة كلهم من قريش )
وفي رواية (لا يزال أمر الناس ماضيا ماوليهم اثنا عشر رجلا كلهم من قريش ) وفي رواية ( لا يزال الإسلام عزيزا إلى اثنى عشر خليفة كلهم من قريش )
قال القاضي قد توجه هنا سؤالان :
أحدهما أنه قد جاء في الحديث الآخر الخلافة بعدى ثلاثون سنة ثم تكون ملكا وهذا مخالف لحديث اثنى عشر خليفة فإنه لم يكن في ثلاثين سنة إلا الخلفاء الراشدون الأربعة والأشهر التي بويع فيها الحسن بن علي قال !!
* والجواب عن هذا أن المراد في حديث الخلافة ثلاثون سنة خلافة النبوة وقد جاء مفسرا في بعض الروايات خلافة النبوة بعدى ثلاثون سنة
ثم تكون ملكا ولم يشترط هذا في الاثنى عشر
For those who don't understand Arabic, Imaam an-Nawawi said that the meaning of the Hadeeth is that the "Nabawi Khilaafah", i.e. the Khilaafah upon the methodology of Nubuwwah, the "Raashidi Khilaafah", would last only 30 years after Rasoolullaah صلى الله عليه وسلم. However, Rasoolullaah صلى الله عليه وسلم himself said that there would be 12 Khulafaa in this Ummah, all of them from Quraysh. So just that alone throws out the notion that Khilaafah could only exist for 30 years, because there weren't 12 Qurashi Khulafaa in those 30 years.
There is a very big difference between a Khaleefah and a king. Muslims are duty-bound to obey the Khaleefah. No one on is duty-bound to obey the "kings" of Saudi Arabia. If the "King" of any country gives an order, I wouldn't attach any more importance to it than what I would to a dog barking on a street corner. He can dream on if he hallucinates that anyone in the Muslim world other than a handful of Madaakhilah will follow him.
Bay`ah is given to a Khaleefah. No Bay`ah is given to a king.
In summary: What Rasoolullaah صلى الله عليه وسلم meant was that the Raashidi Khilaafah would last only 30 years. He did not mean that Khilaafah ended 30 years after him, because that would contradict other Ahaadeeth wherein he said that there would be 12 Khulafaa from Quraysh.
Imaam ibn Taymiyyah mentions the other Riwaayah in his Kitaab. He writes:
قال شيخ الإسلام في منهاج السنة1/515
[ وعن سعيد بن جهمان عن سفينة قال قال رسول الله صلى الله عليه وسلم (( خلافة النبوة ثلاثون سنة ثم يؤتي الله ملكه من يشاء )) أو قال الملك !
"Sa`eed ibn Jahmaan reports from Safeenah, who said: Rasoolullaah صلى الله عليه وسلم said: "Khilaafat-un-Nubuwwah (The Prophetic Khilaafah) is 30 years. Thereafter, Allaah will give His Kingship to whomsoever He wills." (Or in another Riwaayat) "al-Mulk" (the kingship). [Minhaaj as-Sunnah an-Nabawiyyah, 1/515]