To be honest though, and I'll be careful with the way I say this, they had no idea where he was, as he obviously didn't tell anyone where he was going or what his plans were and had no phone to contact anyone, or to try and pin point his location.. the only thing they had to go on was his last known location and his direction of travel. The family reported him missing on Wednesday evening, but the police didn't declare him missing until Thursday morning, assumptions were obviously then made that he was lost while making his way back to the accommodation when in fact he had gone the opposite direction entirely at the harbour.
At first they searched the path from the beach to Pedi, then when they received the CCTV from one of the establishments in Pedi, they started searching the hills behind the harbour (thinking he had gone that way to his accommodation), only when they received the cctv from the private individual showing him walking up the mountain path did they start searching the mountain, but they obviously didn't think he would have made it as far as he did.
Also think about the fact that the area is so large, the heat of the days have been absolutely immense.. and they can't search in the dark, the search teams were searching the commonly used path, and that side of the mountain, unbeknownst to them that he had gone off the path (for reasons unknown, maybe missed the path markers), and ended up going up and over the mountain and coming down on the opposite side of Agia Marina, he could have been intending on looping round to symi so there was the whole area to search, plus the caverns at the top, they just didn't know his intentions so couldn't rule any of it out.
It is really unfortunate set of events, but I do think the Agia Marina have a lot to answer for though, if they had taken the time to look at their own cctv sooner, or search their property perimeter they would have found him, but I don't think anyone expected him to have made it as far as he did.