Just two points here:
One, I've fought against Eurofighters in the F-15E. They are a VERY capable platform, and in some ways more capable than the Eagle. Like everyone has said, the scenario in the link is most likely riddled with behind the scenes information that wasn't printed in the article, like the ROE, bandit cuffs, etc. I will tell you that over in the UK the RAF likes to play using "Fighting Edge", which is an agreed set of ROE in which aircraft that squawk a specific Mode 1 code are "in the game" and can randomly fight each other. The problem is, especially with Eagles at Lakenheath, that our Mode 1s are assigned using a different procedure and frequently we will squawk that code but with no intention of fighting (we'd be out of fuel if we turned-and-burned with every random jet that popped up, and we have other training to accomplish). This results in Eagles that are busy accomplishing a specific mission and random RAF jets that are rolling in behind them and doing victory rolls because they've 'shot down the Eagles'. Naturally, this ends up on PPRUNE and the next round of "we kicked the Eagles' ass" stories starts.
Two, I've fought many front-line fighters in an AT-38, armed only with a gunsight and eyeballs, and like A4s' story, I've achieved gun kills on most of them. It's very possible for nearly any aircraft to get a kill on any other aircraft on any given day, even if there are wicked imbalances in numbers and capabilities. My best was gunning a F-15C Weapons School instructor during a 2 v 2 in the AT-38...and as we merged, I was so close that I could the back of his helmet and see that he wasn't even looking my way. Ooops. "Kill Eagle, level at 14 thousand over Kawich".
So, bottom line? The story is probably true, but like an iceberg there is probably a LOT that is not being revealed in the picture we're being shown.