Yes, this is not clearly explained. The "pronunciation" is more like an indication about how to conventionally pronounce the transcribed text, and not a faithful description of the original pronunciation.

The letters said to be pronounced "ee" and "oo" above, are not the vowels I and U, but the consonants I and U, which in English are written Y and W, like in "yet" and "wet" (i.e. they correspond to Semitic yodh and waw).

So in Egyptian they were normally followed by a vowel, which is not written, so usually unknown. Thus the conventional pronunciation described in the article recommends that instead of replacing the unknown vowel with E, like for the other consonants, one should pronounce Y and W as vowels, i.e. as long I and U, which in English are typically written as EE and OO.

The sign recommended to be pronounced "ah" was some guttural consonant, perhaps like Semitic aleph or ayin. It was also followed by an unknown vowel, so pronouncing it as a vowel is just a convention.

The indications about how to pronounce the vowels of other languages in English always appear comic for the speakers of other languages written with the Latin alphabet, due to the great discrepancy between how vowels are written in English and in the other languages, where it is seldom necessary to give word examples in order to describe precisely which vowels are meant.

While the reason why Egyptian did not write the vowels is uncertain, this fact had a huge importance in the history of the world.

The Semitic alphabet has inherited this feature, together with its later variants, e.g. the Phoenician, Aramaic and Hebrew alphabets. Other writing systems derived from Semitic alphabets, i.e. the European and Indian writing systems, have introduced means for also writing the vowels, but on the base provided by the separate writing of consonants.

All the other writing systems that have been developed completely independent from the Egyptian writing system have been based on signs for syllables or for words, which has resulted in much more complex writing systems than those that have started from the small set of signs needed to write only the consonants.