Well he's only three. Thinking from a three year old's perspective:
He might not have a lot of understanding that kicking will hurt the other child. He might enjoy some game in some other context which involves kicking (football?) and have trouble correctly transferring that interaction to this context.
He might have an excess of energy and the other child is simply in an unlucky sphere. It could have been anyone/anything. It just feels good, and is an impulsive response.
He might feel threatened by someone else being close to him, like he is going to fall off, so he is lashing out in self-preservation.
He might feel threatened by someone else being on the climbing frame, because he believes that it is "his" climbing frame, and he doesn't want anyone else on it.
None of these are excuses or reasons that it's OK to kick, but depending on his language skills you might be able to use them as starting points to find out what is happening before it happens, as you'd want to approach in a different way.
Taking him down, giving time out or leaving the park or whatever other consequence is reasonable, will communicate that you do not like this behaviour, which can help discourage it. But you still have to fill in the gap which is what to do instead. Some children will automatically learn prosocial behaviours by copying others, while some children need more explicit instruction and assistance with finding out what the right thing to do is in certain situations or sometimes in any given situation.
Finding out (if you can) what is behind the behaviour helps you work out what skills you need to work on with him in order to replace this behaviour with one that is more prosocial. For example, if you assume that he has too much energy and needs more directed energetic play to get it out, that will work really well if that is what the problem is. But if the problem is that he feels vulnerable and is acting in self-preservation, then it doesn't matter how much energy he gets out, and actually being tired from lots of physical exercise might make this worse.
OTOH if you assume that empathy is what is lacking, and you do a lot of work about being gentle and caring, and sharing, and playing with other children, this will work well if it's a problem with sharing or empathy. But if it's actually that he has too much excess energy, then he probably won't be able to use those new skills unless he's got that energy out.
(Just examples).