Using Timatic (via the Emirates site) I see:
British passport visiting Kuwait
Visa required.
Visa Issuance: Passengers with a British passport can obtain a visa on arrival for a maximum stay of 3 months. They can apply to extend their stay.
Irish passport visiting Kuwait
Visa required.
Visa Issuance: E-visas can be obtained before departure at https://evisa.moi.gov.kw/evisa/visaPubApp10.do?lng=eng . Passengers must have a printed e-visa confirmation. Nationals of Ireland (Rep.) can obtain a visa on arrival for a maximum stay of 3 months. They can apply to extend their stay.
So, either passport allows a visa on arrival but for Ireland there appears to be the alternative of an e-visa in advance. This is curious. Why would I bother with an e-visa if I can just go without one? Would it permit me to use a different and faster line at immigration? Why is it offered to Ireland but not the UK?