If you stream yourself playing this mod on Twitch you break the non-commercial license in 2 ways:

1) Since streamers often earn a bit of money through subs, donations, etc, they benefit personally commercially. For some streamers, the primary purpose is commercial.
2) Twitch earns money by showing commercials in connection to the stream, which is commercial. Twitch's primary purpose is commercial.

This cannot be what you meant to do when you chose a license, right?

In general, non-commercial licenses are stupid: https://mifactori.de/non-commercial-is-not-open-source/

I'm looking for a proper licence that allows streaming but not changing / republish the work. Any suggestion ?

Well, just don't use a non-commercial license, but use CC BY-ND instead.

I am having trouble imagining a hypothetical example where somebody will profit of your work there. But even if people do profit of it, I don't imagine you would actually personally lose anything. Non-commercial seems to me to solve something that is not really a problem.

If you really wanted non-commercial, you could straight up make a copy of the entire text of CC BY-NC-ND 4.0, and then add at that top that "Nonwithstanding any of the following, streaming or publishing videos of gameplay with this mod is allowed even for-profit". And then call this resulting new license the "MFerrari license". The CC licenses are themselves published under CC Attribution, so you are allowed to copy and remix the license this way, as long as you credit them.

If you really wanted non-commercial, you could straight up make a copy of the entire text of CC BY-NC-ND 4.0, and then add at that top that "Nonwithstanding any of the following, streaming or publishing videos of gameplay with this mod is allowed even for-profit". And then call this resulting new license the "MFerrari license". The CC licenses are themselves published under CC Attribution, so you are allowed to copy and remix the license this way, as long as you credit them.

@thuejk: I want to inform you that I totally stealed this. I hope you're ok with it...
I wanted to do something like this for a long time but had no idea how to do it.
So, I just wanted to thank you (even if you ask me to remove it, which I'll do in that case).

Use away!

Thank you very much! :D