Yea, I'll never second-guess anyone's decision to jump out of a plane. In training, the last step of the inflight fire checklist states something to the effect of "if fire persists - eject".
The F-15 is just remarkably durable that's all, not trying to imply that the Mig-29 is unusually flammable or the pilot didn't do the right thing. It looked like he stuck with it trying to make something happen but the airframe itself was probably on fire by the time he got the fuel to the bad engine shut off, so he didn't have much choice.
FWIW, an uncontained engine failure is what you call it when the engine fails and parts go shooting out the sides of the engine casing. The external casing is reinforced to be able to hold or at least slow down turbine blades if they start coming apart, but at high engine rpm the casing and firewalls/bulkheads may not be strong enough to contain all the bits as they explode from the engine. Ideally, if an engine lets go like that the engine bay is strong enough to be a second line of defense and may contain the resulting explosion, fragmentation, and fire while the pilot shuts down the fuel flow to the engine bay. In practice, sometimes the fragments are moving fast enough to cut through the bulkheads and will damage either the other engine, or fuel lines upstream of the fuel cutoff valves. Or the fire is so hot that even though the fire is initially contained, the engine bay itself catches fire and can't be extinguished. 300 knots of wind fanning an aluminum-titanium alloy or composite flame will turn the whole engine bay into a big blowtorch. In most aircraft, it's only a short time until something critical fails in that situation. In the T-38, what usually goes next are the hydraulic lines to the horizontal stab because they run right along the engine bays on the way to the tail and even a fuel fire in the engines will melt them. A fighter ought to be more durable than that, but a metal fire will eventually burn through even the most hardened structures. The question is how long will it last. The F-15 has proven to last one hell of a long time in some cases.
Of course, it's all about luck too. One F-15E took 14+ ducks or geese down both engines, and flew home burning like a roman candle. Another hit a single bird but the impact and failures destroyed a critical flight control component downstream of the redundant systems, so it went down almost immediately.
