As a very unscientific experiment, I've been going through some EGM magazines, from 1990 onward, to see when it started getting...interesting. Adult fare has been around since the Atari 2600, but the wacko marketing was more recent. This applies to America, plenty of my family grew up in Japan but I never did.
1990, it's mostly all extensions of box art and taglines. Here's about as weird as they got.
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1991, Sega especially starts leaning into "Attitude".
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1992, more of the same. Tubular, radical, far out.
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1993, we're starting to cook with gas. A hallucinogen, I suspect.
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1994....yessssssss.
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By 1995, Weird is Normal, and the Games Are For Horny Teen Boys era truly begins. (3DO being a big example.)
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(Also, there's a notable uptick in implied violence that maybe coincides with the success of Mortal Kombat. You rarely saw anything like it up until Mortal Kombat 2 is poised to take over arcades, then..)
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Not a judgement, just a noticeable change in marketing trends. From this point forward you can find most of the weirder ads already posted above in the thread, American advertisers had a wild time marketing games for the Playstation especially. Tomb Raider, in particular, was a massive get for these folks.