A link to the correct pronunciation, for those so inclined: http://www.focloir.ie/en/dictionary/ei/egypt?q=Egypt
It's a fairly rare combination of letters - only 4 words in the FGB end in pt (Éigipt, script, forscript, and foscript), so it might be considered a "loan pronunciation".
Unusually, I notice that the Ulster audio sample of an Éigipt on focloir.ie is not the same as the audio sample on teanglann.ie, and the "t" is indeed slender in the teanglann.ie version. (The 2 sites usually share the same audio files, and the Munster and Connacht examples of an Éigipt are the same on both sites).
The Ulster example for Éigipteach also uses a slender "t", whereas the Munster and Connacht speakers use a broad t.