Learn Portuguese (Portugal): Este filme é mais aborrecido do que aquele.

To say something is "more [adjective] than" another thing, you use mais + adjective + do que. In this sentence, the pattern is mais aborrecido do que (more boring than).

Is it possible to drop the word "do" and just say "mais aborrecido que"?

Yes! You can say either mais aborrecido do que aquele or mais aborrecido que aquele. Both are completely correct and mean the exact same thing, though including the do is very common in everyday European Portuguese.

Why does the word for "boring" end in "-o" here?

Aborrecido is an adjective, so its ending must match the noun it describes. Because filme (movie) is a masculine word, it takes the masculine ending -o. If we were talking about a feminine noun, like uma festa (a party), it would change to mais aborrecida.

What is the difference between "este" and "aquele"?

They both point out specific objects but show different distances. Este means "this" (a movie close to the speaker), while aquele means "that" (a movie further away). Notice that both are in their masculine singular forms so they can match the gender of filme.