Translation:We are not going to the park, but to the Chinese restaurant.
That sentence feels wrong to me, an American English speaker. Yet, both "in" and "into" can, in certain circumstances be used.
For example: "we'll meet in the restaurant." Compare with "Let's go into the restaurant."
And: "I see him. He's going into the park." Versus "I see them. They are playing in the park."
However: "We do not go in the park," can be used if it is implying either 1) the speakers never enter the park (never have, never will) or 2) they are using "go" as a euphamism for using the bathroom facilities. In the first case there would probably be included the word "never" and in the second case there would be a very particular inflection on the word "go."
It can be "into" for both, or "to" for both. That doesn't exactly make a difference. Maybe the computer mixed the two variants together? It's uncommon, anyway. Maybe we're standing in front of the park entrance and discussing if we're going in or leaving for somehwere else.