Considering multiple JP Hololive girls played it within the last year, in the country where someone hangs themselves via rope or jumps out a building pretty much every day. I doubt management doesn't know what DDLC is or care about the imagery. Tempus has already played scarier games then DDLC, DDLC's only advantage is it is subversive if you somehow can play it blind, but it is also so infamous in its subversion that the majority of people know about it unless you live under a rock or something within the anime/otaku sphere. How Axel doesn't know what DDLC is at all is beyond me to be honest.
It is more a matter if Axel can handle it, and Axel I think is a big enough boy to take it unless their something in this game that really hits home for him like if he knows someone who killed themselves or something. Axel is just too positive and forward thinking to let most things get to him, so DDLC would need some really personal to make him break.
Also DDLC was made by
this guy, who is white as fuck. In fact if I recall he said that he made this game as an intentional farce and break the usual fantasy of harem dating sim VNs by making the entire game go wrong on purpose. It was one of those games that only really worked when it initially came out, because DDLC as a fanbase is every typical anime waifu fanbase just ramped up to 11, especially with Monika.