You’ve got the part but aren’t assembling it correctly and you’re zeroing in the very thing that’s getting in your way.
would mean to speak with someone. In your sentence, the verb would be
To say, have a *conversation with someone * you would say
But 会話 can be used as a noun too. In that case you cannot say
That’s not grammatically complete. To complete it you join the two parts with の resulting in
At this point you’re almost done.
To say this person you would have to say この人.
But what you have is これ+で which means “by means of this”.
So the sentence can be rendered as
With this, simulation of a conversation with a person is complete
You should note that the final copulate だ has been omitted.
Regarding the use of と and の
English and some other Germanic languages stand apart in how prepositional constructs can be used to modify nouns. So in English we can say
A conversation with someone
And it makes perfectly good sense.
However there are languages don’t allow these sorts of constructs. To convey the same idea a relative clause can be used:
A conversation that is with someone
To our English-language ear this sounds cringy. However not in a language like Japanese. The particle の in Japanese is what creates the glue syntactically and semantically joining 会話 and 人と. Resulting in
There are other examples.
The letter to my friend is on the desk.
In Japanese this must be rendered as
This の in 友達への手紙 is serving the same role as the の in 人との会話.