Rootkits could be installed in firmware (UEFI/BIOS). At least in theory. But they'd have to be specifically tailored for each particular motherboard. The possibility of one "infecting" your machine is essentially zero - in practice the only way to get one in your firmware would be to install/flash corrupted firmware yourself, whether a hacker somehow puts it onto the official ASUS download site or somehow gains physical access to your computer motherboard.
Firmware rootkits are always a topic of some concern for Enterprise/IT folks who've deployed tons of (expensive) machinery all based off the same hardwares. But I've never heard of anyone inadvertently/unknowingly suffering from a BIOS rootkit. It might be the sort of malware threat which could gain ultimate control of a computer's hardware and software right at the "bare metal" layer underneath everything else ... but it's also the sort of malware threat which is utterly impotent in terms of spreading itself around or somehow infecting other platforms.
There's been several cases of Sony DVD/Blu-Ray drives installing "rootkits" which impose restrictive content-protection DRM. In and out of the courts, it always hinges around very liberal and very strict attempts to define exactly what "rootkit" means in legal terminology. There are also many (non-Sony) firmware mods for all affected devices which remove these "rootkits" from firmware.
"All opinions are not equal. Some are a very great deal more robust, sophisticated and well supported in logic and argument than others." - Douglas Adams [/Korth]