Did you read everything they said?
If you're running a 32-bit operating system it shouldn't display this message unless you have a Program Files(x86) folder for some reason which implies you actually are on a 64-bit OS because 64-bit uses 'Program Files' for 64-bit programs and 'Program Files(x86)' for 32 bit programs. OR a poorly written program has created the x86 folder even though you're running 32 bit. Check if you're running 32 bit, if you are then you need to check for the x86 folder and see what's inside it. If nothing just delete it, if there's something in there though you'll need to reinstall it elsewhere and then delete the folder.
Either way, RuneMate supports 64-bit AND 32-bit already, it's just highly recommended to use 64-bit, and if you do you also need 64-bit java, hence the message you're receiving about installing it.