I believe game invites are sent as chat messages, but as EChatEntryType.k_EChatEntryTypeInviteGame.

So you just need to listen for the FriendChatMsg_t callback and check for that chat entry type.

Ok but how I only see methods and no events that get trigert am I just stupid?

See https://github.com/SteamRE/Steam4NET/blob/master/Steam4Test/Program.cs#L191 for how callbacks are handled. You'd want to be checking for FriendChatMsg_t.k_iCallback.

I already looked at that code but I think I miss something obvious:
while (Steamworks.GetCallback(pipe, ref callbackMsg)
This line starts a loop for the time Steamworks calls the API giving the output to the callbackMsg variable

Then I need to check if callbackMsg is EChatEntryType.k_EChatEntryTypeInviteGame

but callbackMsg is int and EChatEntryType.k_EChatEntryTypeInviteGame is somethinh different?!

(Also how do I mark code like you did?)

You need to convert callbackMsg.m_pubParam to FriendChatMsg_t, then you can check that object's m_eChatEntryType

I did that:
FriendChatMsg_t friendStatMsg = (FriendChatMsg_t)Marshal.PtrToStructure(callbackMsg.m_pubParam, typeof(FriendChatMsg_t));

However

friendStatMsg.m_eChatEntryType.Equals(EChatEntryType.k_EChatEntryTypeInviteGame)
and
friendStatMsg.m_eChatEntryType == EChatEntryType.k_EChatEntryTypeInviteGame

Don't do anything at all

I also tried
friendStatMsg.m_eChatEntryType.GetTypeCode

I tried everything I can think of now - nothing