Full Immersion
Sometimes the best solution is to dive in and fully become the character your child keeps asking you to do. If you gotta be a horse, might as well be the best freakin horse there is. What this does is changes the mental state. Instead of more interesting or more pressing thoughts jumping into your head, your mind will be too distracted by your masterful performance. This in turn will make you less anxious.
Breathe
We flood our minds with stressful adult thoughts all day. Instead of looking at it as playtime, think of it more as mediation. Focus on your breathing and your posture while you brush dollies hair and sip pretend tea. Clear your mind and relax all the stresses in your body.
Observe
Use this time to stare at your kid's face. Look at how much they've grown. How much they've learned. Try to remember what it was like when they first started playing. Contemplate the miracle that is them.
Ask Questions
Kids are so funny. We all know this. Take a moment to ask them some questions and see how they view the world. You'll definitely get a good laugh and they'll feel happy seeing that they're making you laugh.
Finally, cut yourself some slack. You don't have to feel guilty, we all get bored playing with our kids. Our fully grown brains just aren't stimulated by the play that they need for their brains. But it is important so try and make the best of it. Slow down and truly be in the moments with your kids.