I have found the definition of line in metric space.
It is general but has two problems. Considering about $\mathbb R^2$ equipped rectilinear distance, every line by this definition contains a rectangle and is not a string. Besides, it is possible 3 points in a line not collinear.
Here is what I have thought.
Let $
Definition 0 Point $b$ is said between $a,c$ iff $d(a,b)+d(b,c)=d(a,c)$
Definition 1 A subspace $S$ of $X$ is collinear iff $\forall x\forall y \forall z[\mbox{exist one between the other two}]$
Definition 2 A subspace $L$ is called a line iff it is a maximal collinear subspace in $X$
Definition of collinear set is same as the previous if $|S|\le 3$ but different in otherwise. By this definition a collinear set is a collinear set by the previous definition but the converse is not valid.
According to this definition, it has 2 theorems.
Theorem 1 Every subset of a collinear set is collinear.
Theorem 2 Every collinear set can be extended to a line.
1 holds by definition whereas it does not hold by the previous definition.
2 also holds by the previous definition but requires Zorn's lemma by the current definition.
Hence a Corollary 3 Every set is collinear iff it is included in a line
Finally, by the current definition every line in $\mathbb R^2$ equipped rectilinear distance is actually a curve, no longer contains proper rectangles.
It looks better now. My question:Is it a precise definition?