Both are excellent sentences. In #1, "playing games" is a noun that names the thing that interests the parents. There is no room for confusion so this is, in most situations, the better sentence. In #2, "to play games" acts as an adverb to modify "interested". Though the meaning is clear, this sentence is less useful than #1. There are rare situations where #2 will actually a better sentence than #1, so I'll explain the difference in meaning. Grammatically, infinitives (like "to play") and present participles (like "playing") play similar roles. However, their meanings and uses are different. The difference is that participles are descriptive and have flexible meanings that make them ideal for casual conversation or story telling. By contrast, infinitives are precise with inflexible meanings, making them ideal for careful accurate writing and speech. So, although #2 is a good sentence I would be unlikely to use it because there is rarely a need for precision in such a situation. I would use #2, though, if I wanted to make a precise point that playing games is the specific thing that my parents want to do. They are not interested in swimming! They are not interested in a walk! They only want one thing! They are interested only to play games! Saying it that way hammers the importance of that precise choice so #2 would work.

#1 is correct, except, use UPPER CASE at the beginning of a sentence: Sometimes, my parents are also interested in playing games with us.

Hi Henry, Good question! Number 1 is right and sounds natural. Interested in (something)+ gerund not infinitive. Happy learning Sian

1 is the classical answer. Every test and teacher will say 1 is the only correct answer. But I am a native English speaker and I prefer to use number 2 sometimes. Because when you get to a certain level, you can take ownership of your communication method and speak the way you want to speak, free from narrow-minded rules. Number 2 is easier for non-native speakers to understand; and it makes you sound like a fan of simplicity and oriental influences, to native speakers. For me, number 2 is simply the better way of speaking, irrespective what academia tries to tell me about the language that it does not know any better than me.