Well, for them to have traveled 2.5 m light years in 600 years, they would have to have done an average speed of ~4170 times light speed (12 light years per day!!).
So if that is the case, clearly they possess faster than light travel without mass relays. Also, I'm pretty sure I read somewhere that the game takes place only near the center part of the Andromeda galaxy, not the whole galaxy, so we are only seeing a small part of the galaxy in the game.
If we consider that the starts are similar distances apart as they are in the Milky Way galaxy (~4 light years), it means they can travel to another star in about 8 hours.
To answer your question though, obviously the game won't make us wait 8 hours when traveling each time as that would just be frustrating and annoying, so I would assume they are just speeding those parts up for us
Still, 8 hours form star to star is pretty impressive. Also, weapon and armor research is happening instantly which isn't realistic either, so pinch of salt. 600 years travel time from the Milky Way to Andromeda is really, really impressive.






