American Exceptionalism is a somewhat complicated concept, and it has a few different meanings depending on the context and who's using it. Unlike many users of the phrase, Ike probably didn't think the U.S. was inherently and automatically superior to all other nations. But he did think the U.S. was superior to all others in some key ways.

Mostly, though, Ike used the concept in the sense that America has a special mission, and a special power to help the whole world, to free people from oppression, and to combat evil:

[…] America is today the strongest, the most influential and most productive nation in the world. Understandably proud of this pre-eminence, we yet realize that America's leadership and prestige depend, not merely upon our unmatched material progress, riches and military strength, but on how we use our power in the interests of world peace and human betterment. (II. 3-4)

Ike had seen enough war to know that destructive power isn't the best kind of power, and that the necessity of its use marked the failure of nations to use the more desirable forms of power: diplomacy, economic development, and community building.

Ike's fervent hope was peace in our time.

Or was it "pizza on time"? We'll have to go back and listen to that speech again.