The pun version, which I'd guess was what was intended, would probably be more grammatically phrased as 'How to Promote a Game With a Flare' or 'How to Promote a Game With Flares'. Of course they probably didn't even use flares anyway.
There used to be (still is?) a Canadian fashion magazine (anyone thinking "oxymoron" can just bite it) called, for some reason, Flare. It started up in the 80s, so it's clear they weren't referring to bell bottoms or A-line skirts.
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