How do Type I restriction enzymes work?
To answer your last question first: as long as a restriction enzyme recognises a specific sequence then goes on to cut the DNA it really doesn't matter where the cut takes place, as long as the invading DNA is destroyed.

The WP page on restriction enzymes provides a useful summary of the various classes of restriction enzyme, and led me to a review about Type I enzymes here.

Unlike the familiar Type II enzymes, Type I enzymes require ATP, which they use to power their movement along the DNA, once they have been activated by binding their recognition sequence. The HsdR subunit of the enzyme (R, M and S subunits) contains sequence motifs which mark it out as being related to DNA helicases, which, of course, are able to translocate along a duplex and unwind the duplex.

One particularly striking demonstration of the DNA translocation ability of EcoK1 (a Type I enzyme) is described in 


  Davies et al. (1999) The DNA translocation and ATPase activities of restriction-deficient mutants of EcoKI. J. Molec. Biol. 292: 787-796 doi:10.1006/jmbi.1999.3081


The experiments are based upon the mechanism by which phage T7 injects DNA into E. coli cells.  The phage ejects about 850 bp of the 40 kb genome into the host; the entry of the bulk of the DNA is coupled to transcription, first by host  RNA polymerase, and subsequently by the phage-specific RNA polymerase, once the corresponding gene has entered the cell. If the drug rifampin is used to block transcription then the whole process stalls. This block is overcome if the initial leader of 850 bp is engineered to contain a recognition sequence for EcoK1 whereupon the restriction enzyme is able to translocate the entire genome into the cell at 100 - 200 bp per second. Mutations in the helicase motifs of the HsdR subunit abolish this activity.