This is currently a non-trivial attack to implement and requires the attacker to already have the ability to run applications on the local machine. Coupled with a web server compromise or a SQL injection attack, however, it could conceivably be used as a privilege escalation attack. The basic take-away here is that you need to be sure you've got all your patches installed. Side-channel attacks like this (where the attack targets the system hardware as opposed to the software) are somewhat rare right now, but are only going to get worse as the software gets better at repelling other kinds of attacks.
The scary thing about all of this is that if someone successfully develops a hardware-based attack, it's likely that there's little can be done to mitigate it in most situations. Even if something can be done in the hardware, it will usually require a CHANGE in the hardware to implement the fix.
In this case, I'm not even sure there's something that CAN be done, since the attack is actually targeting hardware that NEEDS to operate pretty much the way it does.