I think you're asking what effect changing the tense of the main verb has on the meaning of the sentence: - I stop eating at 10:00 PM. <= every day, I eat until 10 PM, and then stop eating. - I stopped eating at 10:00 PM <= last night, I was eating until 10 PM and then I stopped eating. - I stopped to eat at 10:00 PM. <= last night at 10PM, I stopped what I was doing and ate. - I stop to eat at 10:00 PM. <= every day at 10 PM, I stop what I'm doing and eat.

Forget and remember are different from other verbs with regards to their meaning when followed by a gerund or an infinitive. Forget/ remember + infinitive usually refer to a small chore or job. Example: I forgot to lock the door this morning. I will remember to buy the milk after work. Forget/ remember + gerund usually refer to a memory of the past. Example: I will never forget seeing the Eiffel Tower for the first time. I will always remember meeting you for the first time.

In your example, the -ing form of the verb is a noun and portrays a skill rather than an action. I forgot to play would mean that you did not play as you forgot but I forgot playing, while it isn't a perfect sentence, would mean you forgot HOW to play or the skill of playing is no longer present in you.