Learn Finnish: Tämä paksu lika on tahmeaa pölyä.

It acts as the subject complement (the part that describes the subject after the verb olla). Because pöly (dust) is an uncountable mass noun, its complement form takes the partitive case (pölyä). The adjective tahmea (sticky) must match it, becoming tahmeaa.

Since lika (dirt) is also a mass noun, why is Tämä paksu lika in the nominative rather than the partitive?

In a standard 'A is B' sentence, the subject (the 'A' part) is almost always in the nominative case, even if it is an uncountable mass noun. The partitive rule for mass nouns being taught in this lesson applies specifically to the subject complement (the 'B' part).

Why does tahmea become tahmeaa instead of taking a -ta ending?

The base adjective is tahmea, which ends in a short vowel. For words ending in a single vowel, the partitive ending is just -a or -ä, not -ta. Adding -a to tahmea creates the double vowel tahmeaa.

Why do the two partitive words have different endings (-a vs -ä)?

This is because of vowel harmony. Pöly contains front vowels (ö, y), so it takes the front vowel ending -ä to become pölyä. Tahmea contains the back vowel 'a', which forces the back vowel ending -a to become tahmeaa.