Can it be right/correct to say the'' typing pool'' is the'' engine''of any company or establishment?

200% sure. I am further to add that you cannot climb the corporate ladder even a step without having typing pool onboard. Whatever stuff/information/data is with you, is the result of typing. You cannot advertise something without typing, you cannot create or develop your newsshelters, messages, emails, brochers, logos etc without typing. You cannot develope and even launch your website wihtout typing. The millions of books on various topic around the world, are the result of typing. Typing is typing, the skill of moving fingers on keyboards.