All the items in the top-level array are wrapped within a JSON object. As the error message says, you need to create a JSON object within your object.
The following code does that for you:
var newItems = [];
var nextTournament = {};
nextTournament.tournamentId1=items[0].json.id;
nextTournament.tournamentId2=items[1].json.id;
nextTournament.tournamentName1=items[0].json.name;
nextTournament.tournamentName2=items[1].json.name;
newItems.push({json:nextTournament});
return newItems;
Note that to reference the value from the previous node I am again using the json keyword. So instead of using items[0].id, you have to use items[0].json.id.