Andromeda is pretty much a normal spiral galaxy. The picture looks a bit like an X-ray image of Andromeda, although why it would show that I've no idea.
Jumping ship to a new galaxy would be a very, very bad way to go. May as well just ditch the whole Mass Effect thing and start a new sci-fi series without any of the baggage if you're going to do that. It also demonstrates a massive lack of the grasp of the size of this galaxy.
If it's going to be a Mass Effect game anything other than a future in this galaxy setting is a bad idea. Since there's no good way around the ME3 ending mess and I really, really don't see the point in a prequel at this stage (even overlooking the lack of time to set it) I'd be happy with just brushing the whole thing under the carpet - saying there was a Reaper war and then forgetting about it entirely and ignoring any consequences it may have had.
By "traditional", I meant "composed of spiral arms in a way that is immediately reminiscent of the Milky Way, especially the Milky Way galaxy map". Andromeda and the Milky Way are both spiral galaxies, but they are classified differently because of their structure and appearance. Andromeda is a type SA(s)b, while the Milky Way is an SBc. Notably, the spiral arms of Andromeda are more distinct and do not adhere to the logarithmic appearance that you see with the Milky Way's galaxy map from the prior trilogy - like at all (although in real life questions still remain about the structure of the Milky Way's spiral, but it would seem odd for them to retcon the galaxy map of all things). Andromeda also lacks a distinct central bar, hence it's classification; however, this may be due to viewing the bar almost directly head-on from Earth. Still, of note is that the image likewise lacks a bar, again distinct from the Milky Way.
Thus, both galaxies are clearly distinguishable from each other. Does that image resemble the Milky Way, even vaguely? No, not really. However, it does resemble Andromeda, and by a lot. And not just the x-ray image of the galaxy, it resembles the infrared images even more closely, and the visual light images as well (although the arm structure is less distinct here given the inclination of the galaxy relative to Earth). It looks like an attempt at an estimate of what Andromeda would look like from a perpendicular angle, which is an angle that we cannot see from Earth, so of course the inclined view of the galaxy from Earth wouldn't match it in appearance exactly.
It seems to be an intriguing image. They deliberately showed the galaxy map for a reason with narrative involving "new regions of space", and it is a distinctly unfamiliar galaxy map.
Is it the Milky Way? Honestly, by that image alone I think we can say no, it isn't. Is it Andromeda? It sure looks a hell of a lot like it. Is it a placeholder? Maybe, but then why show it? Why emphasize it? They could have shown us the classic Milky Way galaxy map and there would be no question, no speculation. But the purpose of the video was to generate hype and speculation with fans, and they deliberately provided a few clues to do just that.