'practicar deportes' is a phrase - 'to play sports'.
"Practicar deportes" mainly means "to exercise sports" or "to practice sports".
Why use Nos interesa and not estamos interesados? Since the category is "Interests", I feel like I'm missing something critical.
The verb is similar to gustar in its use, so you have to think of it as 'playing sport interests us' rather than 'we are interested in sport'.
"Estámos interesados en practicar deportes" is also okay, but it's awfully long.
Why is it interesa rather that interesamos if it's saying that we are interested
As previously mentioned, it is because the verb interesar is similar to gustar in the way it is formed. So it is 'playing sports interests us' rather than 'we are interested in playing sports'. The us is in the nos, rather than the we=nosotros in a standard verb formation.
The subject in this sentence is not desportes, but praticar, and that's singular.
You can compare in English:
- Sports interest us.
- Playing sports interests us.
Practicar is translated by yourselves as playing, practicing. When I wrote playing it’s wrong. Strange