I think we need a bit more information from the OP before deciding if CX are responsible.

I have travelled many times on separate tickets with BA & CX and the 2 times I've been delayed there is always someone from CX waiting to meet me for the connecting flight as the OP requested.

The key here is whether the OP was through checked by CX onto the S7 flight including boarding passes. If they were then CX will provide connection protection. If not then they will still help but it's more tricky.

There is another thread above which describes this process.