Doesn't look like a quest system at all. Looks more like a task system. E.g. You get a task of "Cutting X yews" and as a reward, you get a mystery box and some gold as it is a daily task. A quest is more amongst the lines of "You need A, B, and C items and X, Y and Z skill levels to complete the quest. You can start at point 1, and then head to point 2 where you can speak to this NPC who will give you this mission of speaking to three npcs at point 3, etc. What you could do is change the text "Tasks" into "Steps", but even then it would defeat the purpose of a quest. Players are supposed to adventure and interact with various npcs to find out where they need to go next. If everything is just crammed into a quick-guide then you might as well just have quests that follow the theme of "Speak to Cook, Kill King Black Dragon - Quest Completed".
The idea is nice, the execution is meh.