I think nostalgia and it being original and unknown does give a lot of influence for people, myself included.
The new XCOM is more like XCOM: Enemy mostly known about to people who played the original.
I also think the argument about Space Marine vs original XCOM goes in the way of armour aesthetics, even the demo footage of an early mission they have fairly bulky armour when compared to the coveralls of the original, however the non-aesthetic part that makes it space-mariney is still that you have 4 members vs a horde of aliens while in the original you would actually have more or equal number of units to the aliens and could still have trouble not losing a lot of soldiers, it would be extremely difficult to do an early mission even against a landed small scout or crashed medium scout with only 4 rookies where it would be 1:1 number vs the aliens. Also the emphasis on cover, while cover was a factor in the original it wasn't the do or die factor that it seems in this new game which seems to follow the rules of all games now of being cover based shooters, cover helped in the original but just because you were crouching by that wall didn't mean the alien wouldn't one-shot you and vice versa on the aliens though in the early game it was more like blowing up the aliens cover to kill it.
Yes late game you can wipe out alien bases with 4 guys in power armour for the space marine style (and heck you do go to Mars so you can consider them space marines, even if they aren't wearing any armour
) of playing but it's suicidal to not outnumber the aliens in early missions where they have the great tech advantage.
One thing I hated in the stream though was whenever Jake Solomon kept on saying "remember this is XCOM" whenever a soldier missed a shot, especially when the chance was <50% to make the shot in the first place, I was like "no Jake, this is maths!" . XCOM was missing all shots with autofire on an alien right next to you, or the opposite glory of stray shot flying through two windows to kill a completely different alien then you were firing at.
I wouldn't say original was like SWAT at all, more like soldiers facing an unknown scary threat, I think in the original on the early missions (especially night ones) it had the atmosphere of 'the aliens are out here somewhere and they are going to kill us!' while this new one has more of an atmosphere like 'the aliens are out here somewhere, let's find em to kick their asses and smoke cigars'.