Yes, if you view the Snapchat story of this crush who friendzoned you, you are breaking the no contact rule.
The idea of the no contact rule is to give the other person the impression that you have completely forgotten about them and moved on with your life.
This means that, they can’t have the sense that you are still snooping around and trying to see what they are up to.
If they feel like you are still snooping around, they will not really have the opportunity to start missing you because they will know that you are still around.
If you have decided to apply the no contact rule, you will have to go all in for it to have any chance of working.
This means that your crush can’t get any kind of impression that you are still looking them up or thinking about them.
This also applies to mutual friends that the both of you may have.
You can’t be talking about her to them.
If you do, one or more of them could inform her about it and then she will know that you’re still asking or talking about her.
Again, this defeats the purpose of trying to get her to miss you.
If you want to effectively apply the no contact rule, you should avoid all mentions of her to mutual friends and make sure that you stay away from her in every capacity on social media.