To begin with, your methods of play with your kitten are universal and in my humble opinion harmless - not the cause of the problem.
Note also - I've not read the other answer/s.
I very quickly skipped through the comments and noticed you mention your kitten might be a feral / alley cat. If this is the case could you please edit your question and add/include a brief description of how you came to care for your kitten? It will add context to others who read your original post to better understand your situation and assist those who are attempting to prepare an answer.
There are a few comments I'd like to make in response to your question. I'll itemise my comments first and explain in a little more detail following...
Not wanting to personify your kitten for fear of setting a bad precedent, but kittens are in some respects similar to a human baby and require a number of thoughtful considerations by its human owner or carer, including:
- The kitten has very basic needs - sleep, eat, toilet, play (not necessarily in that order)... then repeat;
- The kitten needs a role model, a creature to set the rules of the litter;
- Many animals respond to the emotional and physical state of their carer/owner.
To explain in a little more detail:
- Basic Needs and Routine
Forgive me if this is obvious, but your kitten has very basic needs at this time in its life. You must provide it with a safe environment for sleep, adequate food and water, time for play and an opportunity to toilet.
Routine is an important element to this. The more consistently you are able to provide for your kitten at the same time every day, the more content it will be. Same feeding time, same play time, same toilet time, etc. This is not always possible and we all do the best we can, so just do the best you can to set a routine.
Play is just one component of your kitten's needs. All must be provided to as regular a routine as you can manage, to ensure a healthy balanced environment for your kitten.
- Role Model and Discipline
While still with its litter and under the care of its mother, a kitten will be taught the lessons of acceptable and unacceptable behaviour. So while still in the litter, an unruly kitten will be disciplined by its mother and the mother will act as its role model.
You must take this role now that it is no longer with its litter "siblings" and under the care of its mother.
Over a period of time you must learn to discipline your kitten and act as it's role model, you must determine what is acceptable and unacceptable behaviour.
Most animals respond well to discipline. Note that some need a "firmer hand" than others, so the extent of discipline is something that you are best to determine for yourself.
Note however that discipline must never be cruel or aggressive, or damage the animal in any way physically or mentally.
When I read your description of your kitten's behaviour after play, it makes me think your kitten becomes over-excited during play and because it has a youthful almost boundless energy, your kitten finds it difficult to calm down.
In some ways human children can become over-excited during play and find it equally difficult to calm down, especially at the end of the day when they are already tired.
To discipline your kitten:
- Take her by the scruff of her neck, as her mother would do. This action has two known effects... it has a physical effect that restrains your kitten and makes it difficult for her to continue the over-excited behaviour and it also has a psychological effect that makes the kitten "feel" reprimanded.
- Say once and only once "No", firmly and without compassion. Make certain the tone in your voice makes your message clear. She will not "understand" the first time so show patience. Do not continually berate your kitten as it has a very short memory and will forget what it has done to deserve the reprimand.
- Take your kitten to a "safe place", for example her sleeping area, then place her in this area and make certain she is contained - that is - she is unable to escape from this space. She will most likely cry for a short time but eventually she will calm down.
After some time has passed, perhaps a half hour, check on you kitten. If she has calmed down, remove you kitten from her "safe place" space and show her a lot of affection. If she misbehaves again, repeat the steps above.
- Animal Response
It is worth noting that many animals respond to the emotional and physical state of their carer/owner. So the more upset you become, the more elevated your kitten's response.
Remember that your kitten is still so young and inexperienced. She is still learning so much every minute of every day and most likely cannot distinguish between your emotion states, let alone hers. She will however understand the difference between elevated emotions and calm emotions.
So, as difficult as this is, always try to remain calm. Your calm emotional state will reassure your kitten.
Good luck with your training.