I won't even ask why you were subscribed to Nintendo Power for 4 years in advance (or why you've still got a photo handy of a 4-year old refund check) . Perhaps the unusual nature of your subscription was the reason for the refund. It's a simple matter to refund an entire year, which has a set, advertised price, but once you're dealing with partially filled subscriptions (which are almost always just a single year), some customers don't understand why they're getting only a fraction of the missing magazines' cover prices in return (having forgotten that the subscription rate offers significant savings over the cover price). It's simply easier for customer service to substitute a different mag.
But to be completely honest, the main reason they tend to switch your sub to another mag is that they don't want to lose a subscriber, regardless of the magazine, since that means a drop in their circulation numbers. The higher the circulation, the more they can charge advertisers for ad space. Some mags have been known to give out free subscriptions just to boost subscriber numbers. Apparently the extra ad revenue their boosted circulation numbers bring was enough to cover the cost of printing and shipping the mag (or more likely a combination of that and a hope that the free subscriptions would later turn into paid renewals.)