How many Integer Operations on a GPU are necessary for one Hash? I thought it was the ALU OPs like here: 
https://bitcointalk.org/index.php?topic=7964.0

ArtForz speaks of much higher values, though: 
https://bitcointalk.org/index.php?topic=4689.msg68933#msg68933

Does the kernel run more than once for a hash? What am I missing?
The ALU OP numbers are correct. The numbers vary based on the video card but are basically in the range of 1,300 to 1,700 operations per double-hash. On the x86, you need more instructions (around 3,700 - 4,500 depending on the exact CPU) but these CPUs can average more than one operation per clock cycle, so you can't convert instruction counts directly into execution speed.

All sensible mining implementations (CPU or GPU) attempt more than one hash at a time. On an x86 CPU, it's typically around four hashes at a time (one per core). On a GPU, it's more like 1,000 - 3,000 hashes at a time (one per core). Hence the superior hashing performance of GPUs.