This opinion is basedon the Kufr duna Kufr Hadith which I will refute.A few things:
1. Ibn 'Abbas was indeed referring to the ayah, as is evident by the narrations in the books of tafsiir. For instance, Ibn Jariir At-Tabari collects some of these narrations with their chains. You can look it up in the verse of Surah Ma'idah.
2. Would you be willing to accuse Ibn Taymiyya and Ibn Qayyim of taqqiyya if I were to present there views showing that they believe not all ruling by other than Allah has revealed to be Kufr Akbar? If so, the please be my guest!
Ibn Qayyim writes in his work "Madaarij As-Saalikiin":
هذا تأويل ابن عباس وعامة الصحابة في قوله تعالى: ومن لم يحكم بما أنزل الله فأولئك هم الكافرون {المائدة: 44} قال ابن عباس: ليس بكفر ينقل عن الملة، بل إذا فعله فهو به كفر، وليس كمن كفر بالله واليوم الآخر، وكذلك قال طاووس، وقال عطاء: هو كفر دون كفر، وظلم دون ظلم، وفسق دون فسق
"This is the explanation of Ibn 'Abbas and all the other companions regarding the verse: "Whoever does not rule according to what Allah has revealed, indeed they are amongst the unbelievers" (Maa'idah, 55). Ibn 'Abbas said: "It is not disbelief that takes you out from the religion. Rather, it is kufr for whoever does it but is not like the one that disbelieve in Allah and the last day", and likewise said Tawuus (from the Taab'iin). 'Ataa said (also from the taab'iin): It is Kufr duna kufr, and Dhulm duna Dhulm, and Fisq duna fisq".
Ibn Qayyim then told what other had said in regards to the verse. He then concluded by saying:
والصحيح أن الحكم بغير ما أنزل الله يتناول الكفرين، الأصغر والأكبر، بحسب حال الحاكم، فإنه إن اعتقد وجوب الحكم بما أنزل الله في هذه الواقعة، وعدل عنه عصيانا، مع اعترافه بأنه مستحق للعقوبة، فهذا كفر أصغر، وإن اعتقد أنه غير واجب، وأنه مخير فيه، مع تيقنه أنه حكم الله، فهذا كفر أكبر، وإن جهله وأخطأه فهذا مخطئ، له حكم المخطئين.
"And the correct view is that ruling according to other than what Allah has revealed encompasses both types of Kufr, the smaller and the greater, in accordance to the state of the one ruling. If he believes that to rule according to what Allah has revealed is obligatory in this particular instance, but deviates from it as a sinner while admitting that he deserves punishment, then this is Kufr asghar. If he believes it is not obligatory, or that he has the choice (to not rule by it), while knowing that it is Allahs ruling, then this is Kufr akbar. If he does not know the ruling and is mistaken, then he is of the same ruling as the others that make mistakes".
3. This is not to say that ruling with other than Allah has revealed is not Kufr akbar in any instance. Indeen, the opposite is true. But it is Kufr akbar in all instances? If yes, do you agree at least that there is a difference of opinion seeing all these narrations from the Sahaba, Taabi'iin and the scholars after them?