From the VP nomination page that you mentioned:
"Due to a large volume of applicants (usually several thousand per academy), the Vice President has authorized the academies to evaluate all applications and rank them according to qualifications. In screening candidates, the academies evaluate an individual's high school or college academic record, results of the ACT and SAT tests, recommendations from individuals who are in a position to judge the applicant's character and academic potential, and physical and medical qualifications. In view of this screening by the academies, it is important that all correspondence subsequent to actual application (e.g., letters of recommendation, high school and college transcripts and ACT/SAT examination results) be forwarded directly to the academy when requested. Do not send this information directly to the Vice President."
Basically what this is saying is that the VP won't be evaluating the candidates at all--he'll leave that up to each academy, and just supply the academies with a list of who applied for a VP nom by his deadline. The academy will rank the applicants, decide if they are qualified etc and then see what nominations the candidate has received (senator, congress, VP, Pres etc). The process of charging candidates to nomination sources is complicated, but someone will off the VP list will eventually be charged to him (assuming he has an opening--can only have 5 people at an academy at a time). You have to apply to the VP, but the academy will decide who gets the VP nom not the VP. Last year, my son's AFA admissions counselor told him he was eligible for the VP nom if necessary (since he had applied and was 3Q), but he ended up being charged to a senator's slate since he had received that nom also. The VP nom is probably the easiest one to apply for--no interviews, no separate letters, etc.
So back to your original question--the letters of recommendation (and transcripts, ACT/SAT scores, etc mentioned also) are just the ones you would normally be sending to the academy via that application process and not something separate. Hopefully this all makes sense!