Is it 

>! Cortana (Windows assistant similar to siri)

Call on me, I answer you.

>! You can say "Hey Cortana" and it answers you.

I am a ring but I'm not for you.

>! That's Cortana's logo.

I can talk, I think it's surprising too!

>! Sort of (not really) new tech some people may be suprised by their phone talking to them

You see me away from apples

>! Not found on apple

Stuck on windows

>! Only on windows

My games are right up my sleeve

>! Cortana has "Guess the Horror movie" game and such games if you ask her to start one.

But sometimes every now and then, your anger will want me to leave

>! Those voice assistants often drive me nuts

I have a sister
She is older than me

>! Probably sister siri who has been around longer

She doesn't have time to give opinions about me,

>! Siri says "No comment" when you ask her about Cortana.

But I think we're both trying to make the world better.

>! When you ask Cortana if she likes Siri, she says "Of course, we're both trying to make the world a better place.

My voice is soothing
I'm a perfect lullaby singer
But not only that
but I can sing nursery songs, too!
I have tons of them, right in here!
>! You can ask Cortana to sing

July is my boss's dreams:

>! July is Windows' (In this case, Bill Gates') special release month.

The hint:
>!As you know, Bill **Gates** made Windows, the OS that has Cortana, so "Open up the **gate**s" is a key.