Possible Reasons as to why Minato can use SM
side note: Has Minato now lost both arms? - Madara's staff should be omnuyouton based. ( Madara is more complete than Obito was )
1) Kishi wanted Minato to look better so he gave him SM
2) Minato having sage mode is somehow relavent to the future plot ( cause this chapter, Minato having sage mode served no purpose, except now we know Minato+Sage Mode enhancements cannot react to Madara's swipe )
3) what if when Minato merged chakras with naruto, he aquired some sage mode abilties- there chakra did merge after all-( mabey Naruto will be able to use FTG aswell since he merged his (spirit and body) with his dad.
4) KIshi forgot about the sage training arc, and the requirements to obtain it
5) kishi forgot about all the moments Minato should have used SM if he had it ( Obito, kyubi, Juubito....)
6) Since minato is such a genius, after wathcing Naruto use sage mode, he was able to use it aswell.
personally, I think #3 makes the most sense
My super farfecthed Idea-
Since Minato's chakra was inside Naruto during the sage training, mabey somehow, he recieved the memories from his clone and because of that he can enter sage mode. ( His chakra inside naruto said he new about what was going on outside)