Do all twin engine aircraft have a critical engine?

No. If your plane has counterrotating propellers, and the props turn toward the fuselage, the plane doesn't have a critical engine. If the plane has counterrotating props that turn away from the fuselage, or both props turn the same way, the plane has one. There's another "critical engine" situation that comes into play even if you've got counterrotating props: if a critical function (cabin pressurization comes to mind) is handled by only one engine, the engine that drives it is critical...then again, it's not that expensive to put a cabin pressure pump on both engines, so that's not real common. One that will make you go hmm...the Diamond DA-42, which drives its props through a gearbox, has a critical engine. They couldn't have put a selectable reverse gear in it? Simply put, the Critical Engine is defined as the engine whose failure would most adversely affect the performance or handling qualities of an aircraft. If, as pointed out above, neither engine would have a greater impact on handling, then neither would be considered the critical engine.