Could I use DataStoreService to communicate between two games? If so, then how?
You can only have the DataStoreService communicate between places within the same game. Remember, each place is not "a game" - places are held within a game.
You would want to create a DataStore system in your game's start place, then have the other place access the same DataStore. I answered another question fairly similar to this one. So below I'm going to have a link to my previous answer, along with other resources that will fully help you reach your goal.
My previous answer to a similar question
The link to the answer above also contains more links to Wiki pages relevant to your question.
Hope this helps!