Legally there is an issue (as I am sure people can see). This company is possibly marketing this activity by advertising the ability to dress up as Nintendo characters and drive around like they are part of a Nintendo game. It sounds like a fun activity, and I see no harm done, but that doesn't mean there can't be harm done.
First of all, if an individual was to be injured during one of these events (even if they weren't part of the activity itself, like an onlooker) they could very easily sue Nintendo instead of this company, either by misunderstanding or some other reason (I don't know the whole legal operation that goes on).
Second, this is Nintendo's IP. It would be like if I started offering phones that looked similar to Apple products, logo and all. People would see these phones and be gullible enough to believe that it is produced by Apple for a cheaper price and sold by a retailer. If not for liability concerns, it is entirely possible that Nintendo would shut this down in the interest of the consumer (I know, I know, very unlikely) not being led into believing this is a Nintendo run organization. This could also be an issue of Nintendo losing future business. If Nintendo were to do something like this in the future, and people had a bad experience with "MariCar" then they might look at this new activity negatively, even if they didn't believe the first one was run by Nintendo.
Finally, these people were definitely using this to get money for their own business. Like I stated earlier, this was most definitely marketed around the concept of being dressed like a Nintendo character driving around in themed carts. I could not possibly imagine they would have received the same amount of business that they most likely did, had they just offered "carting around the city". I am not saying that they made a fortune off of this, but I don't think it would have been as successful.
Morally this is a different story. It could have very much been that a company wanted to provide some fun for tourists and residents alike by providing an experience with characters these people may have been familiar with. It kind of sucks that Nintendo would have to shut this down (but they didn't completely shut it down). If they really cared about the business though and providing that fun attraction that so many of you seem to believe they were doing, they would pay for licensing and the like.