Assuming that you’re only supplying your services to the UAE company (and not making supplies direct to the potential customers in the UK / Ireland) the place of supply is in the UAE. This means that it falls completely outside the scope of the UK VAT system – although I don’t know what (if any) obligations you may have in the UAE.
The second reference you’ve quoted is part of the section on zero rating. The zero rate is technically a rate of VAT, so only needs to be considered for transactions which fall within the scope of the UK VAT system. It therefore doesn’t impact on your supplies.
For completeness, I think that the zero rating is actually clearer in the legislation than the guidance! It’s here: https://www.legislation.gov.uk/ukpga/1994/23/schedule/8/part/II/chapter/7 Essentially what it covers is an intermediary helping a UK business supply services to overseas customers. The intermediary’s services would be subject to VAT were it not for this zero rating, as their customer is based in the UK. 15.4 is effectively pointing out that the zero rating only applies where the intermediary’s UK based customer is supplying their services to an overseas (rather than UK based) customer.