Here is the corner where the missing sign forbidding turns to the right into Maurinkatu should be, if the Maneesinkatu segment was two-way: https://goo.gl/maps/CrzxpLRAtCpEzg1P9

This is a tricky one. At the South-East corner of the park it leads to the side lane in Pohjoisranta which is definitely one-way, so it makes sense that this part of Maneesinkatu is one-way as well.

Another sign: Note that Maurinkatu is definitely one way, so if one would be allowed to drive through Maneesinkatu towards the West from Pohjoisranta then there should be a sign indicating that it is forbidden to turn to the right into Maurinkatu (at the South-West corner of the park)—but there is no such sign, which indicates that driving this segment of Maneesinkatu towards the West is not expected.

That being said, I suppose it's impossible to be 100% sure without asking from some official sources (Trafi, maybe?)