For it to be 'in' the key of G, F#s are required (which is why in Marineville the D min chord sounds odd). For it to be in E min, we'd need F#s and D#s (and of course B major would be the dominant).
Depending on the context of what follows, this progression should really be a stock and classic II, V, I (in C) which is why the pull to resolve to C major is felt so strongly,
I don't think there is a strong pull toward C. I think it pulls toward G or E. If I improvise round this I definitely use F# over the E min to C and then F natural for the Dmin to G which is why I'm not concerned with formal descriptions of key signatures.
but the I is not achieved and instead we hear the E minor as III in C (rather than the final in E Phrygian).
Approaching the tonic from the mediant is a really ugly way of getting there. That's why it doesn't sound C ish to me.
The II, V, I cadence is ubiquitous in Bach for example and is usually modulatory in function,
except for the billions of occasions where II V I doesn't modulate
but of course, no modulation is happening here if we assume a circular progression. As a result, I'd suggest mixolydian as an appropriate modal reading of this.
Mixolydian on G then.
That would be the same key signature as C.
phew. I'm done with this now.
I've got rhythm, I ain't got pitch