[date][hand-written my name]
We are very thankful that you responded to the post for applications about ○○.
We made our first round of decisions based on the documents we received from you, but we are sorry to inform you that you application did not pass.
Finally, we want to inform you that we are praying for the health and success of your activities.
For the record, (1) these letters are generally typed. (2) This one is actually clearer than many which don't necessarily state clearly that you were rejected -- rather you need to decipher it from a 残念 that is nowhere near any verb. (3) They don't come on letterhead -- as is the case with this letter, it's often just unspectacular cheap paper. The better ones put a seal or two on for effect. But basically understand that letterhead is not used in Japan.
Rejection in this process should not be surprising. 公募 (public announcement of positions) is sometimes a mere formality in Japan [and for some job postings in much of the world for that matter]. I was reading at one point an estimate that half of all posted positions are bogus -- as in they already have their winning candidate picked. One thing that amplifies this is that Japan uses an "or equivalent qualification system" that enables universities to hire MAs ahead of PhDs if they like them better for other reasons.