I would imagine the two biggest hurtles are weight and startup time. Steam engines, especially turbines, with all of their supporting equipment can be heavy. So the power density is lower than ICEs, which is a problem when planes need to be light. I'm not particularly familiar with piston/cylinder steam engines like the one in the video, so maybe it would work.

If you wanted a higher efficiency by using a turbine though, there would also be startup time requirements, the larger the turbine the longer the wait. The reason is that the entire mass of the turbine has to equalize at operating temperature before it can be used. Hot metal expands, and uneven expansion can wreak havoc, because the seals have very tight clearances and imbalance in the blades can cause bad vibrations, or even mechanical failure.