Is a highly oxidized element more electropositive than a lesser oxidized counterpart?
There are two definitions of electropositive:


  1:  charged with positive electricity
  
  2:  having a tendency to release electrons


The author is using the first definition, while you are thinking of definition 2, which is the one that usually appears in chemistry books.  

Instead of "makes the atom more electropositive" it could say "makes the atom more electrically-positive".

For example according to the calculation data from Paul J. Schupf Computational Chemistry Lab

Starting from a -1 charge for Cl-  

Adding one oxygen atom (ClO-) increases the charge on the Cl atom to -0.298.

Adding two oxygen atoms (OClO-) increases the charge on the Cl atom to +0.212.

Adding three oxygen atoms (chlorate) increases the charge on the Cl atom to +0.510

Adding four oxygen atoms (perchlorate) increases the charge on the Cl atom to +0.907.

Another example of a different author using the word "electropositivity" in the same way, but who makes the meaning explicitly clear is Interaction of indole derivatives with biologically important aromatic compounds. Part 22. Importance of simultaneous co-operation of hydrogen-bond pairing and stacking interactions for recognition of guanine base by a peptide: X-ray crystal analysis of 7-methylguanosine-5′-phosphate–tryptophanylglutamic acid complex


  MNDO calculations showed that the protonation of the
  guanine N(7) atom increases the electropositivity of the 8-H
  atom [ -0.014 e for guanine and 0.079 e for N(7)-protonated
  guanine],


(bracketed text in original document)   

Specifically regarding chlorine, the term "electropositive chlorine" has been used to refer to Cl+, for example in the Canadian Journal of Research

Another example to look at is from the thesis Synthesis of functionalised silanes for use in the asymmetric allylation reaction:


  In silicon based C-C bond forming reactions the important factor key to their
  success is the ability of the coordination number of the silicon atom to be
  varied. As the number of bonds to silicon increases the electropositivity and
  consequently Lewis acidity on the atom increases.[reference 1]
  
  Upon expansion (Scheme 3; 11 to 13), and ensuing reduction in the s-character
  orbital composition at the silicon centre, the electron density decreases.  
  
  Therefore the electropositivity and Lewis acidity at the silicon centre is
  increased. These tetravalent and pentavalent Lewis acidic silianes have been
  exploited in several Lewis acid-catalysed transformations. Once the shell has
  expanded to incorporate six subsituents it is unlikely for any further extension of
  the valence shell to occur.[reference 2] 
  
  Silicon becomes more positively polarised with the addition of each ligand. As
  this occurs there is a shift in electron density. While the electron density is
  increasing at the ligand, it is decreasing at the silicon centre. The magnitude of
  this polarization is also dependent on the electronegativity of these ligands.


For a very old example, showing the original meaning of "electropositive" to be the first definition, see William Henry's  1823 The Elements of Experimental Chemistry, Volume 1 where on page 229 there is a section "Electro-positive Bodies" which defines electropositive bodies as bodies attracted to a negative electrode and whose inherent electrical state is therefore positive.

Also, there is an historically-interesting article "Electropositivity" and "electronegativity" J. Chem. Educ., 1938, 15 (6), p 291 discussing the inconsistent usage of the term electropositive and advocating for saying "electron donor" instead (if meaning #2 is intended) to avoid confusion.

There is also a 1949 textbook General Chemistry which uses both meanings in the same sentence, using the older meaning to define the newer meaning:


  The electropositive character (tendency to go to a more electropositive condition) of elements, in general, decreases across the periods


Overall, it is confusing to use the word "electropositive" contrary to the definition that usually appears in recent chemistry books, but not really wrong.