[davem]

I'm not sure CT sees the games as having anything to do with Middle-earth - actually this is pretty much the reason he didn't include the early drafts of TH in H0M-e.

Wikipedia has

When Christopher Tolkien began publishing The History of Middle-earth, a twelve-volume series documenting J. R. R. Tolkien’s creative writing process in the creation of Middle-earth, with texts dating from the 1920s to the 1970s, he made a conscious decision not to issue a volume detailing the creation of The Hobbit. According to him, The Hobbit was not originally a part of the Middle-earth universe and was attached to his father's earlier, far darker legendarium only superficially, although the existence of The Hobbit forever altered the legendarium. The tone of The Hobbit is much lighter and more appropriate to a children’s tale than that of J. R. R. Tolkien’s other writings.

As Christopher Tolkien was not going to embark on a published study of The Hobbit, the task was given to Taum Santoski in the 1980s. Santoski had connections to the Marquette collection of Tolkien material, which is where the original manuscripts reside. He died in 1991, and ultimately the task passed to John Rateliff. Although Christopher Tolkien did not work directly on The History of The Hobbit, the work will be in a very similar vein to the "literary archaeology" of his History of Middle-earth.[4]

Rateliff submitted a finished draft of the book to Christopher Tolkien, who, approving of the work, gave The History of The Hobbit his personal blessing to be published in association with his father’s other works.