The problem is not building the thing (though it is one problem), it's that if you're using this as a crane you're moving an entire baseball field with a decimeter if not centimeter-scale precision.
I have no intuitive feel for how heavy 250 tonnes is, but even if current crane tech can move that weight with centimeter precision, they're explicitly marketing this for tasks where the current tech has issues with access, which implies they don't think it competes directly with traditional cranes on their own territory, but does work well enough in specific circumstances to be an option.
Maybe its a bad idea overall, or unrelated business model issues render it a dead-end, but beating the current product in every concievable metric in every concievable use case is not necesssry for a product to be a success.
a) powerful enough to defend against wind acting against such a huge object
b) responsive enough to change their thrust vector (power & direction) such
that the associated PID loop can operate within some reasonable set point
boundary
I guess this is a long way to say i don't think it'd be easy or cheap, but i don't think they'd have to make a break through innovation to make it possible.
This is going to be a light, fragile airframe with much bigger 'sail' in the form of the airship - its the size of a stadium.
Nothing short of a rocket engine will be able to keep it in place.