1) Helping your mom means to do chores from time to time=NO
2) Helping your mom means doing chores from time to time=YES
Sentence 1) is not grammatical. Form: Doing something + means + gerund [etc.]
The meaning of means here is: implies or calls for. That is the semantic meaning of the verb mean in this sentence.
Sentence 2) Not grammatical at all. There is another meaning of the verb mean that is: to intend to do something. I intend to so something can be expressed as I mean to do something.
If we rewrite sentence 1) with the meaning of the verb mean that means to intend to do something, we can see it would not make sense:
- Helping your mom intends to do chores from time to time=NO. That's easy to see.
Now, here's an example with: mean + to-infinitive.
- I mean (intend) to finish this explanation before I go food shopping.
I hope that clarifies the issue for you.