Not directly but it may have had a hand. October and November are shaping up to be big expensive months and I think Square Enix in conjunction with Sony may be trying this thing called management where they space a new IP far enough away from some of the bigger releases so that their sales aren't adversely affected.
Remember Forspoken is a PS5 console exclusive for 2 years. Both Sony and Square Enix have financial reasons to not let this game be released to the wolves during a busy season and forgotten about a few months from release.
Well, the game is also coming out on PC day one....AND was to be released before God of War until it was delayed. Forspoken wouldn't have had any impact from GOW release. And actually, outside of annual rinse and repeat Call of Duty, this season is one of the most dismal seasons we have seen in ages.