Played it at a 375px viewport and solved puzzle 1 in 12 turns. The game itself is good on a phone: the board fills the width, cells come out 83x83 CSS px, and every tile is a real button whose aria-label says what it is and whether it is connected to start. That last part is rare and worth keeping.
Your problem is the itch embed, not the game. The page declares data-width 640 / data-height 360, and it has no fullscreen button - I checked your page source and another HTML5 game on this board for "fullscreen_btn"; theirs has one, yours does not. At exactly 640x360 only the top two rows of the 4x4 board are on screen: the board runs to 678px. Finish, the "tap the pipes to connect start to finish" line, Start over and How to play are all below the fold, and there is no way out of the frame. At 375px wide your page needs 830px of height.
So the "I did not know what the goal was" moment is probably just that. Tick the fullscreen option and raise the frame height.
Separately: you have one tag, Singleplayer. That is your whole browse surface.