The UAE imports everything, and I mean darn near everything, except oil. Its a very upper-echelon wealthy place and is just starting to sprawl. In a few years you won't have any problems finding what you need somewhere but there just isn't a large enough computer enthusiast market to support business.
I spent about a month there when I was in the Navy, Dubai was cool and all but it seemed overly produced. There was no real "down town" kinda place as there were no mom-n-pop stores. The huge mall there was cool but the closest thing to a computer/game store was the Virgin Record (which had a HUGE techno section).
Give it some time man, more people will move in and more business will spring up that isn't main stream commercialized. For now, since you're a builder, try to talk to one of the plumbing trade subcontractors and see if they have a few extra feet of what you need.