To hazard a guess: I imagine that young Japanese are far less likely to be strict pacifists and, thus, are liable to be sympathetic to Abe's push for constitutional reforms, which can be framed as "modernizing" Japan, whereas elderly Japanese - at least, the left-inclined ones - who grew up in the shadow of WWII, are far more likely to be strict pacifists or to take issue with militarism. Further, Abenomics is rather radical in its thrust - constituting a break from ill-advised half-measures and the schizoid nature of post-90s crisis management in Japan - so I can see why young people in Japan would back the LDP, who are seeking to bring Japan out of its ~30 year period of malaise.
The LDP is a terrible party and Abe is a bit of a nutcase but they deserve credit for reviving the Japanese economy.
I think a better explanation is that turnout among the youngest age groups is utterly dire so those who do show up are unusually 'committed'.
Although the successes of the Abe government are undoubtedly factors as well.
