Does a research competition with monetary prizes count as commerical use?
Disclaimer: I am not a lawyer and this is not a legal advice.
In general, this depends on at least the following factors:

particular text of the formal license under which the dataset is provided
the laws of the country where the parties (licensor and licensee) reside
definitions that are used to determine whether the activity is considered to be commercial or non-commercial if the actual license text is unclear about it
status of the organization where the research is conducted

However, usually, the commercial purpose has the connotation of direct income generated from the goods or services produced with the help of the licensed content. In the case of the research work that happen to win a certain competition, I would argue that would not be considered a direct income. Thus, should constitute non-commercial use.
From the Creative Commons study on non-commercial use, the following definition of the commercial use is very common:

… in any manner that is primarily intended for or directed toward commercial advantage or private monetary compensation.

I would argue that no academic research has the primary goal of monetary compensation. Winning in the competition for an academic researcher usually is &quot;collateral damage&quot;.

To reiterate,

The definition of commercial and non-commercial use is license-specific; therefore, without the text of the license, it is impossible to determine whether a certain way of using the licensed content is legal or not.

If in doubt, consult a lawyer or use the legal services that most educational institutions provide.

The use for academic research that might/did win a competition is very likely to be within the non-commercial use clause of the license.