Imo there is nothing about looking as premade graphics on the old one.

If anything, it suits its media better. Ofc they could remove some of the shading (its just a bit too much imo) to make it more "unique-looking", but its far from generic.

From a designer's view it looks unique enough and you can see that there was work behind it (not that the new one doesn't have the same amount of work applied to it), and its very powerful as it should be for an e-Sports team.

The new one is a very good logo too, but I don't think it works that well as others for e-Sports. You could argue that there is logos like SK's, very simple and people like it, but keep in mind SK is a recognized brand, the logo is old - even tho it was reworked to current design trends - so its easier to like it. It depends, lets see its applications. Maybe with some gradients (even tho its an effect I wouldn't use for any logo besides an e-Sports logo), some cool texture background...

The new one just really lacks identity - unless it stays around for a bit of time, the team gets bigger and so... which isn't exactly what you expect when designing a logo, that the client's success will determine the recognition of your logo.

Also, if you think the old one looked generic, this new one looks even more imo, like if you googled "Warrior head vector" on Google Images.

Maybe if they added the name of the team in the logo, perhaps. Nothing stops them for having variations for different applications too. Like one with a name for promotional use, and the one that OP posted for profile pictures and in-game overlay, for example.