Personally I think it is allowed. To me, the keywords are there to let you know what exactly a unit or model is. Kroak has the Slann keyword because, even though there's no mention of "Slann" in his name, he's still a Slann. Likewise, the Engine has the keyword because it does have a Skink Priest on its back, therefore allowing that rider to fulfill the role of a Skink Priest within the Formation.
I think a good place to look for this would be the Clan Eshin formation. In it, it requires the formation to be led by a Skaven Assassin, makes sense, they're the leaders of the Clan. But why would a formation led by, say, Dave the regular assassin be more effective and more well-trained than one led by Deathmaster Snikch himself when he's both a better assassin and the actual leader of Clan Eshin, making him a better leader for a formation? Well if you act under the assumption that keywords don't count, then Snikch officially becomes a worse leader and assassin than his subordinates as he cannot act as leader to his formation. But if you allow Snikch to lead the formation because he has the Skaven Assassin keyword, then it makes perfect logical sense, he can indeed be this leader.
Comparison aside, think about it this way. The Skink Priest title has literally no use what so ever beyond making the bearer of it eligible towards leading the Shadowstrike Starhost. If the Engine can't lead this formation, what is the point of including that keyword? The only logical reason is that it allows the Engine to lead this formation.
And on the subject of stealth that Angel understandably brought up, I don't know about you but I'd imagine that a reality-warping device capable of stopping time and shattering physics could be used rather easily to conceal your formation until it reaches the battlefield. Hell, I'd imagine that the engine could make the formation even more stealthy than if they didn't have it because it can just fracture reality itself enough to hide the formation.
