Nope, doesn't work that way. The game dev is offering a networked service (community,support,etc.)in his name/trademark/brand and therefore is therefore liable for the data protection, it doesn't matter at all if the dev is the data holder or not - that's up to the dev to manage contractually with discord.
The concept of "not holding the data, not liable for the data" has been turned down by various high court rulings by now - Amazon and Microsoft amongst others have tried it and lost.