Yes the photo might be an old one, couldn't really say either way but it seems that the old pier was not demolished in 2010 as google claim the attached image is June 2019 and the remains of the pier are clearly still there.
Most was demolished, quite why they didn't finish the very last bit I don't know. Probably just too dangerous or expensive, I wouldn't be surprised if getting rid of the remaining bit would involve lots of explosives, divers or both - it's well into an area that is always underwater. What's there now is a tiny fraction of what was.
The pier in 1973 at low tide:
After the pier originally closed there was many efforts to save it, all of which failed, and it was left to get into worse and worse condition. The straw that broke the camels back was the storms of 1987 - as not predicted by Michael Fish - that almost certainly took it beyond economic repair then. It dragged on for years after that with the West Pier Society (or some such similar name) making various moves towards restoration, but not making any actual progress. It was clear by the end of last century that it was never going to happen. Then more collapsed at various times, there were two (I think) fires - leaving a rusting skeleton that was a serious hazard on the promenade, beach, foreshore and in the water. The pier was actually a grade I listed 'building' so couldn't be actively demolished until English Heritage de-listed it, which they finally did and finally it was demolished.
Each time I went to visit my mum there was another slice of decline to observe. It was, in a way, quite a sad thing to see because as a lad I'd had some good times on that pier.
As to whether it's still a new photo? I doubt a Reuters press photographer is going to swim out to the few remaining rusty girders with his $6,500 Nikon D6 in tow, climb up with some little scallywag who shouldn't be there, get his shot and swim back. Na, it's old, I suspect really quite old.
I actual stood on that pier in 1973 (when only the shore-side part of it was still open) with the crappy Zenith B SLR camera I'd bought with my previous year's birthday money and took photos of Sid James and all the crew running around making "Carry On Girls". The film unit's stills photographer came over and chatted to me and gave me several reels of 35mm colour neg film - quite an expensive luxury from my perspective at that time.