Closing something as off-topic isn't obtuse: the close reason for off-topic questions says (emphasis mine):
Questions on Gaming - Stack Exchange are expected to generally relate to gaming, within the scope defined in the faq. See the FAQ.
The only way one could be confused about it being off topic is if they read the close reason and lost the ability to read/see after coming to "relate to gaming".
Closing something as not constructive is weaker than closing it as off-topic: it implies that the topic of the question is good, it's just asked in a way that'll invite discussion or argument. It's more subtle than closing something as off-topic, and—speaking as a moderator on the progenitor of the "not constructive" close reason—opens the door for debate on whether the question was asked in a constructive manner.
Because if my game recommendation question is asked in a way that meets all the requirements of constructiveness (outlined in "Good Subjective, Bad Subjective"), it should be opened since it's no longer inviting "opinion, debate, arguments, polling, or extended discussion."
Ah, but an astute Gaming.SE user will say, "but we decided that all gaming recommendation questions, no matter how they're worded, are going to solicit those things so we actually made it explicit in the FAQ that these are off-topic here." And we're back to using the off-topic reason and the user having to be clued into the debate you don't think they have to know about.
To give an example:
What should I be looking for in an open-world RPG?
I recently purchased Skyrim, and I've really enjoyed it. The open-world nature of the game, where I can avoid the main quest line and focus primarily on side quests and other objectives, is something that I can see myself playing for a hundred hours or more.
I'd like to find other games like Skyrim that I can play after I'm done with it. How can I identify open-world games like Skyrim? Are they marketed in a specific way, or are there certain developers who focus on such games? What has been your experience in finding open-world RPGs?
This question is constructive: it hits all the points in "Good Subjective, Bad Subjective". However, it's still a game recommendation question, and it's still off-topic.
On the other hand, the "off-topic" close reason is meant to be concrete: you shouldn't be asking the question because the FAQ specifically says they're not welcome here. It's why questions that are closed as off-topic are docked one point: the person asking it didn't even bother to check the FAQ.
So the rule of thumb is: if it's explicitly off-topic in the FAQ, close it as off-topic. If the question is on-topic, but worded in a way that'll solicit debate, discussion, and/or argument, close it as not constructive. Game recommendations are explicitly off-topic in the FAQ, so they should be closed as such.