How can one-dimensional strings form point-like particles with no dimensions?

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Assuming that string theory does not rule out point-like particles such as quarks, how can a group of one-dimensional objects be seen as having no dimensions at all?
 
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Strings are much smaller than the particles we currently observe, so for all (practical) matters and purposes they are 0-dimensional - except compared to other strings.

Strings are 1-dimensional, so 0-dimensional objects are "ruled out". However, in M-Theory objects of all sorts of dimensions (0, 1, 2, ..., N) are supposed to exist.
 
So quarks would not really be 0 dimensional. Thanks!