The arrow of time in a thermodynamic system should be thought instead as a statement about time-reversal invariance. For example, in classical mechanics, based solely on the particle motion one cannot tell if time is going forward or backward. In the same way, in an open system one cannot tell which way time is flowing based on the change in entropy alone. In essence, entropy does not define the direction of time in an open system.
However, this is different from asking about why time doesn't run backwards in a refrigerator. If you think of a fridge as something that decreases entropy over time, one can think of its time-reversed partner as a heater which increases entropy over time. Hence, in thinking of the system as a refrigerator, you've already selected a particular time direction. Nobody is stopping you from defining time to flow in the opposite direction, but asking why time doesn't run backwards in a fridge isn't really a well-posed question. Saying time flows backwards is a relative statement; you have to tell me what "backwards" is relative to.
EDIT: My answer seems to be unsatisfactory, so let me try to elaborate.
First, what is meant by time? It is a 1D parameter that controls properties of objects (eg position). You can think of each physical property (object) independently having their own time parameter.
Now, it is interesting to note that the microscopic laws of physics are time-reversal invariant. This means that the form of the equations don't change from $t\rightarrow -t$. However, you'll still get qualitative differences, such as velocity $v \rightarrow -v$ under time-reversal. Hence, a particle moving to the right will be moving to the left under time reversal. Hence, what time-reversal invariance means is that if you look at a clip of a particle moving forward in time vs moving backward in time, you can't tell which one is which. So, if we have don't know which way time should be going, we can just pick one of our choosing.
Then, we can just choose a time direction for every single particle in a collection however we want. But wait a minute; if I watch all the particles move, then clearly their time directions should all be synchronized to my time. Hence, we stumble upon a key property of time that it depends on the observer. The observer is the one who sets the forward flow of time for all particles. Hence, to come back to the question, if I, the observer, call a system a refrigerator, I have already selected a time direction for it, which makes original question itself ill-posed. In other words, the reason why the refrigerator's time and the spoilage of food and the influence of gravity all have the same time direction is because their time direction is assigned by the observer.
Now, the second law states that entropy in a closed system must increase over time. Hence, just as before this defines a time direction for the property of entropy. Now, somehow we must synchronize this time direction with that of all the other time directions, again via an observer. The magical thing, as the article you cite notes, is that for some reason the time direction selected by the second law is always the same as the time direction selected by observers in the physical universe. But, as the article also acknowledges, nobody really knows why. At least, it doesn't seem that this is a derived consequence by any well-accepted physical theory, but rather a postulated coincidence (like the equivalence of inertial and gravitational mass).