It is pretty common for boxers' eyes to look red and irritated. People ask me all the time if there is something wrong with my dogs' eyes because they are red. This is because of the drooping eyelid of most boxers. The inner eyelid shows or is exposed and is red naturally. This is what you are seeing, the inner eyelid, not really "red eye." Also, when playing or excited, blood rushes to their heads and this can cause the eyes to look bloodshot and red as well. Not to worry about it.
As long as your dog is not showing signs that they eyes itch, and the eye goo is clear of grayish in color (not green or yellow) then there is no problem. If the eye goo is greenish or yellow, a trip to the vet is in order.
Here is a website with lots of information on canine eyes, etc., if you are interested.
http://www.petshealth.com/library/eyedog.html
Good luck.