I've been reading up on GPGPU for some time now and I was wondering if only arithmetic operations work on the GPU for parallel processing or can any thread work on it? For example: if I had many threads that contained code for player updating that I wanted to parallelize, would it work on the GPU or no?
The GPU is a specialized processor, so it can't do anything that a general processor like a CPU can do. Also, it works best for computation jobs where you want to do the exact same procesing on a whole collection of data (SIMD = Single Instruction, Multiple Data processing). It's also only really suitable where most of the work consists of doing computations, and not for things where for example I/O is the bottleneck.
Whether what you want to do with it is suitable for doing on a GPU is hard to say, it depends on what exactly you want to do.