In the final confrontation between Willy and Biff, the two men argue about the conflicts that exist between them. Biff attempts to lay down his side of the dispute, not in reconciliation as much as truce. Willy, however, sees this attempt to end the argument between them as an act of spite.
A natural interpretation of Willy's feelings suggests that Willy is simply hurt by Biff's announcement that he is going to leave and never come back to his parents' house. He is hurt and feels that Biff is hurting him intentionally, so he claims that Biff is acting in spite.
This is not true from Biff's perspective. Linda has told Biff to leave. Biff has also realized that he has been carrying around a fantasy about himself and a grudge about his father for too long. He wants to let go of both and is willing to say that Willy is not to blame for either.
Willy will not accept Biff's truce and refuses to really hear what Biff is attempting to say.
Spite is not Biff's motivation, however, and that is clear. His motivation is quite the opposite. He is motivated by sorrow, penitence, and love (for his mother at least, and maybe his father too).
Willy is a deeply conflicted guy. He failed Biff in the past by not encouraging him enough in school, by letting Biff believe he was somehow special and above everyone else and by having had an affair that Biff discovered. He feels that Biff's lack of material success is partly his fault as a father, but outwardly expresses his frustration that Biff has never made a success of himself.
Willy is trying to separate himself from his own remorse and Biff's failure and place the blame entirely on Biff, so he accuses Biff of behaving spitefully. If Biff's failure to live up to Willy's expectations is entirely Biff's fault through his own spitefulness, then Willy doesn't have to accept responsibility for his own influence on his son and his personal failures.
At the same time, Biff has held resentments against his dad for past wrongs, including finding out about his father's affair and for letting Biff believe he could have whatever he wanted without working for it. But of all the characters Biff seems to have a more realistic sense of himself and what he wants and does not appear to be acting spitefully so my answer would be no. Biff's failure is not the result of spite, but of a lack of personal accountability. Biff does seem to be struggling to change that in himself, and his character appears to show the most growth.