Do all restriction enzymes have palindromic recognition sites?
The article cited in the question goes on to discuss the different classes of restriction enzyme, for which the recognition ‘style’ differs. Not all recognize palindromic sequences.

Type II restriction enzymes 

These have been divided into a number of subclasses (reviewed by Pingoud and Jeltsch). Those regarded as orthodox — which are the ones generally used in DNA cloning — appear always to require palindromic sequences in their recognition sites, although those in some other classes do not (see list here). 

This statement is subject to the proviso that you regard as palindromic 5-base recognition sites, such as AlwXI, GCAGC, and others with a ‘non-conforming’ central region, such as ApaBI, GCAN5TGC. The reasons for including the latter (which provides an alternative way of defining the requirements of the recognition sequence) can be seen by examining the symmetrical manner enzymes of this class bind the site, which can tolerate a non-symmetrical central region. This is described in more detail in an answer I gave to another SE question on restriction enzymes.

Type I restriction enzymes:


  …cut at a site that differs, and is a random distance (at least 1000 bp) away, from their recognition site. Cleavage at these random sites follows a process of DNA translocation, which shows that these enzymes are also molecular motors. The recognition site is asymmetrical and is composed of two specific portions—one containing 3–4 nucleotides, and another containing 4–5 nucleotides—separated by a non-specific spacer of about 6–8 nucleotides. 


Type III restriction enzymes:


  …recognize two separate non-palindromic sequences that are inversely oriented. They cut DNA about 20–30 base pairs after the recognition site.