"GPS" is used in the article simply because it's a nice buzzword that non-aviation people know, but it doesn't necessarily pertain to how the exact method of navigation is implemented in the aircraft. In aviation, the umbrella term for this kind of navigation is "RNAV", a somewhat counterintuitive backronym for "area navigation". Basically, it means your aircraft is capable of determining its position (subject to some quantifiable error) and navigating to an arbitrary set of geographic coordinates, rather than following ground-based navigational beacons. How the position is determined depends on the exact kind of RNAV system you have installed. Most modern airliners have a highly accurate dual- or triple-redundant inertial reference system (IRS), in addition to (usually) two GPS receivers and a couple of ground-based navigational aid receivers (usually VOR/DME). The aircraft's flight management computers (again, usually at least two) then use a complicated set of filtering algorithms to combine these inputs and compute an actual aircraft position and a CEP (circular error probable) value, which is then interpreted and displayed in the cockpit as a navigational precision value. RNAV procedures are designed for a minimum required navigational precision. Therefore, the loss of GPS reception doesn't manifest in the aircraft suddenly losing all sense of where it is located. Instead, the FMCs simply interpret it as the loss of a source of position data and carry on using the remaining good sources. Even without GPS, the inertial reference systems are highly accurate and rarely exceed more than +-1NM positional error even on very long flights. To further limit IRS drift, most modern FMCs automatically use the ground-based navigational aid receivers for periodic adjustments of the IRS platforms. They autotune a nearby VOR/DME station, read off magnetic radial and distance information and use that to correct IRS drift.
This all before we even get into systems such as WAAS or SBAS, which are specifically designed to quickly detect and correct GPS transmission errors. High-quality aircraft GPS systems also include a set of features called RAIM (Receiver Autonomous Integrity Monitoring), which means the GPS equipment will perform a receiver and predictive signal integrity check prior to commencing a critical phase of flight that might be dependent on the GPS equipment operating correctly.