Software vs Interactive Internet: Expanding Definitions?

I have a computer game that I just purchased on a disc. The disc is hardware. The game, would be software, right?

What if I have a hardware disc, that guides my computer on how I can play a game with another computer through the internet and that other computer changes its plays depending on what I do on my end. What would you call that? Its something that goes beyond the limits of my interacting with a software program on a disc. Is that still referred to as software? Surely, there is a distinction between the two and word definitions that signify that difference. They’ve both been referred to as programs but that’s a huge umbrella that doesn’t tell us (the royal us) much.

If anyone faintly understands my question, please reply.