If there is an Apostate from Islam who has fled darul Islam to Darul Kufr, then is it still obligatory to execute the apostate or is it okay to treat him as just a regular non muslim?
An apostate remains an apostate whether or not he is located in the Dar al-Islam. He is never treated as a normal non-Muslim.
وتختص الردة - في الاصطلاح الفقهي - بالكفر بعد الإسلام. وكل مسلم ارتد فإنه يقتل إن لم يتب ... ولا يترك المرتد على ردته بإعطاء الجزية ولا بأمان، ولا يجوز استرقاقه حتى لو أسر بعد أن لحق بدار الحرب
Apostasy is defined - in the terminology of jurisprudence - as Kufr after Islam. And every Muslim who apostatizes will be executed if he does not repent ... He will not be allowed to remain on apostasy by receiving jizya or by asylum, nor is it permitted to enslave him, even if he is captured after running away to the Dar al-Harb.
Ibn Khatal, Miqyas bin Subabah and Abdullah ibn Sa'd ibn Abu Sarh were apostates who had fled from Medinah to Makkah. At the conquest of Makkah, the Prophet ﷺ had commanded for them to be killed and not forgiven - unlike most of the remaining disbelievers.