Interns don't get benefits and often don't get paid. I don't know why you would expect vacation time for an internship. But even working at McDonald's or Kroger you accrue PTO. I worked part time at the YMCA as a lifeguard and still got PTO.
I didn't expect it, but I got paid for working full time for months, and was offered health insurance, but no sick days or other PTO, just paid per hour for however many hours I worked.
I worked at Walmart full time for most of 2015 unloading trucks all day long and didn't get any PTO, and even got denied months in advance to take a day off for my birthday.
Idk, everyone I know who has worked at Walmart accrues vacation time even part time. This is in Kansas and Virginia, though. Not sure what state you worked in.