Why would a company mention these things? A small part of me feels
that they do this because they're trying to hide something bad, for
example the work sucks so they got an xbox.
They are not trying to hide something bad. If you have never worked for a tech startup that is bootstrapping, this is a common practice.
These days, the job (work you do) matters less than the company (people, not organization) you work for - in other words, do you fit in their culture? They are trying to show what kind of people you'll be working with because this goes directly towards job satisfaction and the likelihood that you will stay for the long term.
By the way, not all startups have such xbox/beer culture.
What is the difference between a company where people where suits and
act seriously vs one's where they don't and have fun together?
You answered the question right there - the difference is the people and by extension the company culture.
Beyond this, nothing much. Microsoft, Oracle, Google - they all develop software and have competing products. Culture, however, is completely different. Part of the culture is the "perks" you have the office (like the xbox) and the kind of clothes you wear.
I'm not saying people who wear suites don't have fun, I'm just saying
if a client comes into the office wouldn't it look bad if there were
nerfguns around? At least that's what was explained to me.
The kind of "clients" that would walk into a startup's office are most likely investors and VCs; these people invest in the team and not necessarily the product. By definition a startup is just a bunch of people trying to find out if there is a market for an idea it is not a company.
You are thinking in a very singular approach to work; where there are well-defined clients and the client/employee relationship is dictated clearly (for example, I work at a bank and here, such a relationship is clearly defined).
Not all companies have the same culture.
The bottom line is this - If you don't like the company culture, chances are high you won't enjoy working there. You should be thankful that the company culture is on full honest display; its a great way to know (other than the work you do) will you fit in with the people around you.