The vast majority of countries don't require visitors to declare criminal convictions when seeking entry. The UAE operates a 'visa on arrival' system for British passport holders, which is little more than a way of charging an entry fee. (i.e. there are no real formalities).
The UK is prohibited from sharing information about criminal convictions with other countries (under EU privacy laws) unless there are specific reasons for doing so. (e.g. when there's a threat of terrorism). While a conviction for drug dealing might be flagged up to UK customs up when someone is seeking to re-enter the UK, there wouldn't be sufficient grounds to advise other countries of the conviction.
Anyway, despite having read your link several times, I can't see anything there which says that he's been involved in drug dealing. As I read it, it only says that he was under the influence of drink or drugs at the time of 'attempting to commit arson'.