If you notice, the two statements that are given are textbook statements. Textbooks always use these statements to describe an electrostatic field and a conservative field. This essentially means that the student is familiar with the two statements (unlike JEE Assertion/Reason statements). So the question here is, does statement 2 explain statement 1?
I'll point out one thing: - Statement 2 is about Conservative fields and loops; while statement 1 is about electrostatic fields and paths.
This is what the question focuses on, according to me. How will work across a loop being zero imply that work done is same across any path? Is an electrostatic field always conservative?
I know it's an insult to students to ask them the last question. It's THAT simple. But still, people will have doubts. After all, an induced electric field is NOT conservative! but wait a minute! Is an induced electric field electrostatic?
This is how we are supposed to learn - ask yourself as many questions as you can... you want to clear up the basics.
So, carry on with the answer and the discussion.