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Google translate is giving you a different words than you hear in that lecture because it is translating to standard Arabic language not Egyptian dialect.
Saudis do understand Egyptian dialect, so they will be able to understand you. But may be you wouldn't be able to understand Saudi dialect.
some of the difference between both dialect the word you mention (now) Egyptians say (delwa'ti - دلوقتي) while Saudis say ( alheen - الحين) but in Standard Arabic it is (ala'an - الآن)
also there is difference in the pronunciation of some letters like: the letter (Jeem - ج) like in the word Jamaal Egyptians pronounce it like ga in gate (Gamaal) but Saudis pronounce it Jamaal and in standard Arabic it is Jamaal - جمال.
another example of the difference pronunciation of some letters: the letter (Qaaf - ق) like in the word Qalb - قلب Egyptians pronounce it like (a - أ) aalb but saudis have two pronunciation of the same letter some words they pronounce it like (ga) like in this word Qalb = Galb and some words they pronounce it like (Qa - ق) like the word Qareb - قارب ( boat)
about which one is closer to classical Arabic, well you can't really tell which one is closer. but what I think that there is no dialect closer to classical Arabic. and even if there is one, it will still have very big difference between that dialect and Standard Arabic.
about which dialect is the most spoken and anyone in the Arab world could understand I think it is the Egyptian dialect. This is because a lot of songs, shows, etc. are produced in Egyptian Arabic and also a lot of Arab speakers get to see Egyptian TV.
if you want to read the Qur’an, be able to read state documents, books, newspapers... etc, then you should learn Modern Standard Arabic.
if you want to be mostly understood in the Arab world, learn Egyptian dialect.
if you know specifically where you will go and live, learn the dialect of the people of that country.
