The bike's big advantage is going down hill. On the other hand the low gearing of such wide tires bikes makes for slow speeds (Through probably faster then walking).
One advantage he did have over the dogs is the dogs time on the trail is regulated.
http://iditarod.com/race/rules/
For example rule 13:
Rule 13 --Mandatory Stops: A musher must personally sign in and out to start and complete all mandatory stops.
Twenty Four-Hour Stop: A musher must take one mandatory twenty-four (24) hour stop during the race. The twenty-four (24) hour stop may be taken at the mushers option at a time most beneficial to the dogs. The starting differential will be adjusted during each teams twenty-four (24) hour stop. It is the mushers responsibility to remain for the entire twenty-four (24) hour period plus starting differential. The ITC will give each musher the required time information prior to leaving the starting line.
Eight Hour Mandatory Stops: In addition to the mandatory twenty-four (24) hour stop, a musher must take one eight (8) hour stop on the Yukon River, including Shageluk in odd numbered years, and one eight (8) hour stop at White Mountain.
None of the) mandatory stops may be combined
Rule 16:
Rule 16 --Mandatory Items:A musher must have with him/her at all times the following items:
Proper cold weather sleeping bag weighing a minimum of 5 lbs.
Ax, head to weigh a minimum of 1-3/4 lbs., handle to be at least 22 long.
One operational pair of snowshoes with bindings, each snowshoe to be at least 252 square inches in size.
Any promotional material provided by the ITC.
Eight booties for each dog in the sled or in use.
One operational cooker and pot capable of boiling at least three (3) gallons of water at one time.
Veterinarian notebook, to be presented to the veterinarian at each checkpoint.
An adequate amount of fuel to bring three (3) gallons of water to a boil.
Cable gang line or cable tie out capable of securing dog team.
Functional non-chafing harness for each dog in team and a functional neckline
I know Rule 43 is not a factor here, but it is the Anti-Poodle Rule:
Rule 43 -- Dog Description: Only dogs suitable for arctic travel will be permitted to enter the race. Suitability will be determined by race officials.
I do NOT know how the race made these rules applicable to the biker, they are designed to protect the dogs. No dogs, no need for any concern for their health thus the mandatory stops may NOT apply to the cyclist (and the Race MAY have applied them to him, but then the race may say the rules applied to people in the race and a cyclist is just someone running on the same course, which is through public land and thus the race official can NOT stop him from using).
Thus he may have been able to beat the dogs because he was carrying less then the sleds must carry and need not stop as required by the race for the dogs.