If you define fun by “having a blast” then we are talking about the same thing. Why wouldn’t a game be valid if it’s about delivering a message above moment to moment action? Strip the message away and obviously it’s lesser for it. Because it’s not a message plus an entirely separate mechanical system, it’s about what everything means in context. Rather than focusing on making flashy combos, it’s more interesting to ponder over what is it supposed to represent and what is actually happening.

It’s a little funny though that I did consider Spec Ops as another example, and that I have seen people judging it the same way that you are doing to Hellblade, that it was a mediocre military FPS, but many rebutted that even its lackluster gameplay is supposed to contribute the commentary. In the same way you praise of Spec Ops, I don’t think Hellblade is nearly as bad in that aspect as you say, As an action game it is serviceable, but the action is not the point.

If you argue for serious games but only in the context of the gamification of business and education, you are still glossing over a whole multitude of media that is more about exploring ideas than moment-to-moment thrills, something other media have in plenty, and something which games have incredible potential for. You are thinking of typical games solely in terms of pop culture. There is a lot more to a medium than pop culture and strictly functional tools, and you are making that to be a massive abyss where nothing has worth.