Most of the Estonians with Russian names do identify as Russian, even if they aren't necessarily Russian nationals. It's an ethnic group, these are ethnic Russians.
> The reason it looks different, is because they're Estonian, so the name will be different
This is false. It's spelled the way it is spelled because that's how Estonian government wants names spelled. Also, because it would be awkward to interact with a society where most people do not know the Cyrillic alphabet.
He's quite literally an Estonian national, go check the FBI report that was released.
https://en.wikipedia.org/wiki/Russians
In Estonia these people are referred to as Russians too, because that is what they are and what they identify as.
And, to your point about them being called Russian in Estonia, I've heard them called "Russian speaking" more than Russian. Then, again, the Estonians I know take a pro-integration position on the matter, so it could be a difference.
Writing Russian names in Estonian script does not make them Estonian names.
Correct, but it does not suddenly make them another nationality. Also, it's not spelled as you spelled it for a reason -- it's Estonian you're looking at. Not Russian. The reason it looks different, is because they're Estonian, so the name will be different.
My second point, which is pretty clear in the first place, is that a nation of people illegally occupied by Russia for decades, isn't keen on being labelled as Russian.