I think its a recommendation that he repeats kindergarten but I dont think he can be made to repeat...?
If the teacher is recommending that he repeat, she probably has some pretty good reasons for it - the main one being that she thinks, with the skills he has now, he cannot be successful in 1st grade.
If this was my child, I would have him go to first grade. However, if he goes on, you need to really be prepared to work with him, ALOT over the summer, and in the next school year, to provide extra support for him.
Its hard, because if he is a little behind with his skills, you want to work with him on his skills, but if he is active, you dont want to take away from his play time and activity time. If you search on the internet, you can probably find some ideas for sight word games which involve movement - versions on basketball, or races, etc. One that I just made up :) : Take 10 site words and put them on large cards in large lettering. Make a matching set. Place the 10 words around your yard. Put the other cards in a stack, facing down, on the porch. Your son must pull a card from the stack, run to find the matching word, and then run back to the porch. Repeat this until he has found all the matches. Time him as he does it, and track the times, to see if he can beat his best score.
I would also meet with the first grade teacher and explain the situation and see what she can do in her classroom that would help him. If there is more than one first grade teacher, ask which one is best with active boys. If the first grade teacher requires alot of seat work - your son will have a really hard time.
I would definitely want my son to go on - but you have to put in alot of work, and get the right teacher, or he will be more frustrated and unhappy next year.