Not so, but only because of rules about the notation that are not stated. The dot in the top left (which I am assuming is one of the initial positions that the game gives you, from the darker background color) is, due to its shape, necessarily a size 1 ship. It does not continue downwards. Similarly, the initial position on the left-middle shows it going upwards. The initial positions not only tell you that there is a ship going through that location, but also in what direction, if it's the end of said ship.
Yeah, maybe you should put that closer to the top. It took me 5-10 minutes to realize that I hadn't scrolled down quite far enough to see that extra rule.
It's especially easy to miss if you're already familiar with the original 2-player version of Battleship, since there's no such rule in that game.
It appears to be European; you can switch to a Dutch and German version of the site.
Maybe this is European vs. American rules?
The German version of the Battleship page gives Rule 1 as "Die Schiffe dürfen nicht aneinander stoßen" which seems to mean that they cannot touch each other (not simply that they mustn't overlap).
The point of the no touch rule is that you can use your brain: from the hit information, you infer water areas where the enemy must not have ships.
Under the Milton-Bradley rules, the players can just clump their ships together into a small area; it's just more or less pure guessing. If you hit two squares side by side, you cannot infer that they are sections of the same hull; they could belong to two parallel hulls, or to two ships "parallel parked". It's dull to be able to infer next to nothing.
Yeah, that can be confusing - just updated the "show mistakes" code with a special-case "Ships can't touch diagonally" message when that happens, hopefully that'll help.