Is this an argument?

The word's meaning varies depending on its context.

argument — /ˈɑːɡjʊm(ə)nt/ — noun

1.an exchange of diverging or opposite views, typically a heated or angry one.
Similar: quarrel, disagreement, squabble, fight, difference of opinion, dispute, wrangle, altercation, dissension, war of words, contretemps

           disputation, controversy, tiff, barney, bust-up, spat, ding-dong, falling-out, row, afters, rammy

 

   2.    exchange of views: debate, discussion, discourse, 

 

   3.    a reason or set of reasons given in support of an idea, action or theory."there is a strong argument for submitting a formal appeal"
Similar: reasoning, line of reasoning, logic, case, defence, justification, vindication,
explanation, rationalization, evidence, reasons, grounds, argumentation, polemic, assertion, declaration, claim, plea, contention, expostulation, demonstration

 

    4.   In mathematics and logic: an independent variable associated with a function or proposition and determining its value. For example, in the expression y = F ( x₁, x₂ ), the arguments of the function F are x ₁ and x ₂, and the value is y.

           ◦another term for amplitude.

    5.    In lingusitics:any of the noun phrases in a clause that are related directly to the verb, typically the subject, direct object, and indirect object.

    6.    Archaic usage or in academia: a summary of the subject matter of a book.
Similar: theme, topic, subject matter, gist, outline, summary, synopsis, abstract, precis, plot, storyline


Personally, when I use the word, I'm more likely to use the second or third meanings.

It was funny, and it was about arguing, but I would say it wasn't quite an argument. I tend to think of arguments as more heated, more passionate and less reasoned.