The vowels are there because that's how Egyptologists pronounce Egyptian.

The various "Egyptian alphabets" that you can find on the internet or in elementary school textbooks are typically based on the uniliteral signs of Middle Egyptian, or more rarely Late Egyptian. They're reproduced with varying degrees of accuracy--the chart you've linked, for example, incorrectly lists the aayin arm as the phoneme /b/ and for some reason thinks that Egyptian has a /v/ phoneme--but that's usually the gist of it. These tables for schoolchildren, in an effort to present an "alphabetic" Egyptian language that corresponds precisely with English, also sometimes break up signs that are identical. For example, in the chart that you've got there lists /s/ and /z/ as if they're separate signs, when in fact those are just different forms of the door bolt sign. It also lists the folded cloth as the letter C, when in fact in Old Egyptian it was probably /s/ and in Middle Egyptian is more or less indistinguishable from the door bolt /s/. And so forth. There are other errors or oddities, but it's not worth going into them. And more important to the question, the inclusion of vowels is not one of them per se, although the attribution of vowels to particular signs in that chart is another story.

Egyptian has three types of "phonetic" hieroglyphics, that is signs that indicate a phonetic quality rather than being logographic or a determiner (a single sign can be used as any of the three, and most are). These are, broadly, the uniliterals, biliterals, and triliterals. The last two are sometimes just called multiliterals. These group are distinguished by the number of syllables that they represent. Biliterals represent two syllables, triliterals three, and multiliterals either one syllable with a vowel (unexpressed and usually just voiced by Egyptologists as the /e/ phoneme) or just a single consonant.

Egyptian is not an Indo-European language, and it certainly isn't English. It lacks consonants that English has, and it has consonants that English doesn't. For example, while the shelter and twisted rope are both listed as /h/ in that chart, they're two separate consonants, h (/h/) and ḥ (/ħ/) respectively. Middle Egyptian then has two more voiceless fricatives, ḫ and ẖ, the pronunciations of which are not entirely certain. And here's part of the issue. We don't know how Middle Egyptian was pronounced. I mean we do, and we have a much better idea of Middle Egyptian than, say, Sumerian. And comparison with later languages like Coptic helps fill in some of the gaps. But the fact of the matter is that compared to Greek or Latin we know relatively little about Middle Egyptian pronunciation, and we know even less about dialects and changes in the pronunciation over time.

As such, when Egyptologists pronounce Middle Egyptian it's basically an approximation. And Egyptologists do pronounce the signs listed as vowels as vowels. While Egyptian did not indicate vowels by Middle Egyptian there do seem to be semi-vowels, as well as sounds that don't exist in Indo-European languages that are difficult to classify. For example, the aleph vulture (listed as /a/) may have been some form of the glottal stop--its pronunciation is highly debated, and the Egyptian sound appears to be related to the Arabic aleph, which is also complicated. Similarly the aayin arm was probably /ʕ/, which we simply can't make as a consonant in English (though Semitic languages like Arabic have it. NB that in Modern Hebrew it is indistinguishable from the glottal stop). Egyptologists tend to pronounce both as if they're the vowel /a/. The double reed was probably the semi-vowel /j/. But the single reed seems to have sometimes indicated an actual vowel, or something so close to /i/ that we're not sure what else it would be. Similarly, the wau chick (and the curlicue sign, possibly a rope coil, which is listed as a separate sound in your chart but is just an alternate form of the quail chick) were /w/ but also appears to behave as a sort of semi-vowel in some words. Typically Egyptologists pronounce it as a W or the vowel U depending on the word. So, for example, the wau in ḥwt-nṯr, "temple," is pronounced by Egyptologists as oo ("hoot-netcher), even though that's not likely to resemble very closely how the word was pronounced by actual Middle Egyptian speakers.