There are two things this method accomplishes that may have been desirable to its designers. First, it encouragesonly those who have easy access to a fax machine, who in most cases are white collar workers of a certain incomelevel, or if a home computer user, a fairly sophisticated one with fax capabilities. Second, it discourages anyone who has to make a long distance call to transmit the form, thereby increasing the chances for local entrants/winners.
If that was the audience being targeted, I'd say that's incredibly clever. Even if so, I think they should have had a "print" button on the bottom. Never underestimate the inability of a user to figure out how to create a hard copy of the form, especially when this mechanism is rather unusual. One wonders if the hard copy of the faxed entry is or could be designed to be used as an address label to mail the winners their bounty. If the contest involved a drawing, a hard copy could provide the entryto physically draw out of the "drum." If the contest operator wanted to be really devious and avoid retyping the information, the web page form would covertly submit to a database as it printed out for the user to fax, but only the fax would qualify the entrant for the contest. Then you'd have the best of both worlds. (But if you get caught and criticized for doing that, you didn't hear it from me. Heh.)
By the way, mine is not a legal opinion. Check applicable contest laws before embarking on such.