Yes a strainer is a kitchen utensil.
Strainers which are a kitchen utensil are also known as a colander that is used to strain water or other liquid after you cook food.
For example when you cook spaghetti you need a strainer which is a utensil that allows you to pour the spaghetti into the strainer while allowing the water to go through the strainer and out into the sink or bowl.
A strainer is a utensil used in the kitchen that is most used to strain liquids away from other ingredients but also to occasionally sift fine ingredients away from larger ingredients.
Other examples of kitchen utensils are measuring cups, measuring spoons, knives, forks, spoons, whisks, ladles etc.