I was asked to write two impromptu essays, each less than one hundred words. The first essay was on why I want to be part of the company. The second one was on how I can help the team. This is how I remember writing the first essay. -

"I'd like to be part of the company for two reasons. First, I'd like to impart my skills and take part in advancing the objectives of the team. I believe that a company that promotes intellectual diversity by hiring people with different specializations is bound to be successful

Second only is my desire to improve my skills by applying the theories that I've learned to actual practice."

Not sloppy, even though it doesn't really say much (advancing objectives, applying what you've learned, etc., all a given). But that's OK because it's pretty typical.
Not sure if 'impart' is the best word for the simplest expression 'use.' Don't get caught in the trap of fancy sounding words.

This is a little bit too much about you and not enough about the company. Stress how much you have followed their growth and how proud and eager you would be to be a part of their future. In the same vein as using fancy words, don't get caught up in sounding 'correct' when they really want to hear that you are dying to work for them.
Bragging about yourself is the second question, which you don't have here.

But I'm nit picking, and I think it's fine. If you don't get the job, think about some of this for next time.

It is somewhat a normal text book answer that sounds like it was cut and pasted from some management or recruitment handbook.

It is not sloppy but not very impressive for a hiring manager.