The shinobi do really well against the hippodrome units because they can also heal and they do bonus damage against melee units. So, against horsemen and any of the hippodrome units, they are going to be doing quite well. At the same time, Macedonians don't really like making archers early on. It's very expensive if you go for the range and war camp. You could make an archer range but then you're really locked in to the archers on that production building. The range and war camp is giving you way more options when it comes to military that you can produce as the game goes on. So, it's a little bit awkward for the Macedonians to try and go for archers early on in the game.

The Hippodrome Horseman has an aura giving +2 damage to all friendly cavalry, making them better against Shinobi.

Macedonians should be able to win in the Castle Age if it gets there. Like your Riddari can beat samurai. Japanese players at the highest level get good at dragging past the Castle Age, because if you hit Imperial Age that's where Macedonian's economy starts to fall apart.

Japanese mounted samurai should be able to contest Macedonian Riddari, but the spears (Atgeirmaðr) are a completely different ball game.

Kura Storehouse will scale nicer into a TC-inflated timing with farms than Macedonians are capable of; you don't really see Grand Winery for good reason.