It's pretty awful considering that he could have been electrocuted by potentially any electrical appliance, as you guys rightly point out.

Could we expect anything better from the tabloid press, though?

Sadly, as Adam and Stefan point out in the story, a similar line was also taken by The Guardian, The Telegraph and The Times. Looks as if it came from a wire bureau which figured, "Hell, there's lots of news about tragic kids and lots of news about video games around this time of year, we'll run with that". The mainstream hacks went with it.

We're still waiting to hear back from any of those mighty organs of news...

I think in some ways though, the other headlines aren't quite as bad:
Boy, 7, killed after plugging in Game Boy
Boy, 7, electrocuted in Thai hotel while charging game
Game Boy kid electrocuted in Thai hotel
British boy, 7, electrocuted while on holiday in Thailand

These are really just statements of fact, as he was killed when plugging in his Gameboy in Thailand.

These ones:
Connor, 7, Killed By Gameboy
KILLED BY HIS XMAS GAME BOY

Are totally wrong as the Gameboy (as far as we know) wasn't directly responsible for his death.

but would they refer to him as 'Lamp kid' instead of 'Game Boy kid' ?

I doubt, had he been plugging in a lamp, they would have run with the story at all. There are (I calculate based on a population of 60 Million and an average life expectancy of 70) around 2,500 UK deaths a day... the papers cover very few of them - even the ones that are caused by misadventure.