What is needed for electronic and interactive board & card game equipment?

I'm a little bit computer illiterate here about electronics. We have 2 computers in our home, one is a desktop and another is a laptop. My sister and I living in the same home would like to play scrabble, and card games with each other on different computers. Someone told me we would have to go online in order to play each other. We had hoped some way we could network the 2 computers, to do this. Or would we have to purchase a play station, or an xBox to interact with each other in our

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