Do your have the field set to save and load terms?
the taxonomy query added to your arguments should look something like this: see https://codex.wordpress.org/Class_Reference/WP_Query
$args = array (
'post_type' => 'exercise-database',
'tax_query' => array(
array(
'taxonomy' => 'your taxonomy here',
'terms' => array($term_id), // <= this needs to be an array of term id, can have a single value
'operator' => 'IN'
)
),
'pagination' => true,
'paged' => $paged,
'order' => 'DESC',
);
But before you go to the trouble of creating a custom page template for every category you should think about using the template hierarchy built into WP. If you have a custom post type and you add a custom taxonomy for the CPT then you only need to create 3 template files: archive-{$custom-post-type}.php, single-{$custom-post-type}.php and taxonomy-{$custom-taxonomy}.php. It would be a lot easier than building and doing custom queries for every category.
