Lots of businesses like to claim being a "startup" as it brings connotations of innovation, dynamism, coolness, being the "next big thing" etc. There are many senses of the word, and it can be used in different ways (e.g. I work at a small business which has some elements of startup culture, and it's not an incorrect way to give people a sense of what it's like here - but we're definitely well established) but I think often being one of the "cool kids" is part of the motivation.
