Adjective for one meaning of "argument"

Although the term argumentative can be used here, the more common term for this type of work is discursive writing. Here's a definition the adjective discursive from Merriam Webster:

1 a : moving from topic to topic without order : rambling

1 b : proceeding coherently from topic to topic

2 : marked by analytical reasoning

Note that this usage derives from the last two definitions, not the first!!!

Here's an example taken from the Cambridge University website for IELTS teaching:

• The texts may be written in different styles, for example, narrative, descriptive or discursive/argumentative.

The adjective argumentatious is less influenced by the far more common sense of argumentative. It is also far less common, but is given by say Dictionary.com.

I'd be tempted to use the compound argument-based. Check how it is used in this article say by the North-West University.

It is correct to use argumentative writing in your example. Here argumentative means using reasoning.