My guess is that you're running in a Linux-on-Linux soft virtualization environment such as LXC or OpenVZ where all virtual machines run above the same instance of the Linux kernel. In this kind of environment, kernel parameters (such as the sysctl parameters that you can set via
/proc/sys) apply to every virtual machine. Therefore only root in the host environment can modify those parameters, root in a virtual machine cannot.
If you need to allow more I/O requests, you'll need to ask your VPS provider. But they'll probably say no, because if 65536 isn't enough for you, you should probably be on a bigger, non-virtualized setup where you aren't sharing I/O.