Clever, but this is naive and a case of 'Orientalism in reverse', as one Thesis available in PDF online makes clear. I read this before becoming a de-facto Christian and bought into Corbin's project that Christianity was lacking politically against Islam and even that it inevitably led to Nihilism. However, now to be honest I find the claims against and misunderstanding of Christianity astounding; this is from a scholar with such a good reputation.
I've seen this crudity with Alan Watts as well unfortunately.
One would be safer reading Christian Theology to see what it's about (and its relationship to Nihilism, Islam, etc).
One could, if they are being serious, try Schmemann, Evgeny Lampert, Milbank, Stanilaoe, Eugene Webb, DB Hart, Khaled Anatolios, V Lossky, Bishop Barron, David Tracy, Florovsky, Cyril O' Regan, W Desmond, Torrance, RW Jenson, Zizioulas or many others.
There's really no point in attacking straw men of Christianity and attacking heretical forms of 'Christianity', which Corbin does in the book. Taking down Tillich's frequently heretical views and a kind of simplistic Descartian 'Christianity' doesn't mean much.
For historical surveys on Christianity you can see DB Hart again, Warren Carroll, Justo Gonzalez, Jaroslav Pelikan or countless other knowledgeable scholars and then you can compare and contrast more fairly.
'Mystical' Islam needs to be contextualised within the matrix of history as well and Corbin ignores many essential points.