What qualifies you to fence in a wheelchair competition? I am wondering because of this video from the Paralympic games 2012, where the two opponents walk around quite a bit and only use their wheelchair while fencing.
Yes, participants in wheelchair fencing in the Paralympic Games need to be disabled.
The Paralympic Movement provides sport for people with disabilities. They list ten eligible impairment types, and in order for an athlete to compete, he or she must have a primary impairment that belongs to one of these impairment types.
Each sport in the Paralympics has specific classifications with medical eligibility rules. For wheelchair fencing, which is administered by the International Wheelchair and Amputee Sports Federation(IWAS), these rules are found in the IWF Rules for Competition: Book 4: Classification Rules. The book spells out tests that certified Classifiers use to determine whether or not an athlete is eligible.
Classifiers administer functional and bench tests to place athletes in one of five sport classes: 1A, 1B, 2, 3, and 4. On one end of the spectrum, class 1A participants are "athletes with no sitting balance who have a handicapped playing arm. No efficient elbow extension against gravity and no residual function of the hand which makes it necessary to fix the weapon with a bandage." At the other end, class 4 participants are "athletes with good sitting balance with the support of lower limbs and normal fencing arm."
At the Paralympics, fencers compete in two categories: Category A is for fencers in class 3 or 4, and Category B is for fencers in class 2. There is a Category C for fencers in classes 1A and 1B; this category does compete in some international competitions, but is not normally in the Paralympic Games. (Source)
The IWAS has a formal protest process. If someone feels that another athlete has not been classified correctly, they can issue a protest, and a jury of Classifiers will investigate and rule.
The video that you referenced is of the gold medal bout at the London 2012 Paralympic Games in the Men's Individual Sabre Category A, the category for athletes with the least impairment.