You are right, I saw the phrase 'portable gaming being killed by smartphones' and I think the word gaming and smartphone in the same sentence sent shivers down my spine. But it is a fair point that the distraction of internet browsing can be enough to keep people from feeling the need to game. Though for me personally, I recently realized (when I temporarily had no books to read on my Kindle) that I would be scrounging for any old crap to browse on my phone just to help pass time rather than actually be interested in looking at something (obviously this is not the case for everyone, but for me I have plenty of opportunity to browse the internet at a desktop, so have no actual need to do so 'on the go'). So I really would have appreciated having a portable gaming system.
Why smartphones are replacing handhelds is simple, it's not because smartphones are replacing handheld/console style gaming, it's more like, think back to the early 00s. You have a long bus/train/plane ride, or you don't eat enough fibre and spend too much time on the toilet. You could play snake on your Nokia tankphone, you could read a book or you could play a game on a handheld. Handhelds were a good option, smartphones aren't a better gaming option, but you don't have to game while travelling or on the toilet, it was just one of very few things you could really do conveniently. Due to smartphones you can now check your e-mail, surf the web, watch a tv show or movie, listen to music, or play some pretty basic games that are still significantly more complex than snake.
It's not that smartphones are equally good gaming devices, it's that because everyone has a smartphone, we carry with so many options to pass the time that carrying around a fairly large and heavy second device purely for gaming is actually significantly less convenient.
Ultimately when it comes to gaming, handhelds offer a significantly worse experience than a console/PC. So now with so many more options thanks to smartphones, why not dedicate your time gaming to a comfy sofa or chair and a nice screen/monitor, with better sound, no interruptions, no stopping and starting the game constantly, better graphics etc, just a far better experience, and do something else while travelling around.
That is why smartphones are replacing handhelds, it's not just about gaming.