UAE relationship with Japan is mainly for exporting crude oil and natural gas and importing CARS and heavy mechanical parts, electronics and equipments. Not very much apart from that. Maybe because of huge language barrier.
Thinking the UAE Way
UAE loves Car LoL
Okay so; apart from this
They would have thought of making good technological relationship with some Asian country and when they thought Japan suited them the most.
Factors which might have played are following according to me:
Japan has neutral/peaceful secular political relation with other countries so far so improving relationship with Japan seemed to be logical.
In long term since it is not going to get involved into any political twist and turn. The trade(resulting from good relations) will be stable.
Japan has good tech infrastructure which might be helpful to UAE in future to move its economy off the oil.
Also Japan's JAXA is new and is keen for opportunities this motive from UAE will bring about good relationship & trusting capabilites of JAXA is evident from Japanese work culture.
Opting for private companies is no where in list.
It will be better if you ask - Why UAE did not opt for X country over Japan.
With other countries he already have good relations so far.
And it was the good time to give JAXA the work since they needed one.Instead giving it to someone which reaps out nothing as compared to JAPAN. Building new relationships are always favourable if possible without harming current ones.
After oil ends their economy will be based mainly on relationships so more the number(of relationship hands) better the success rate and lower the risk.