TacoBiscuit: I just changed every password on all my important stuff just now.
I think one of the main things is that you keep your email password long/hard to guess and secure, and that it is not used anywhere else but that particular email log in.
So definitely don't use the same password in gog.com, Steam, nudegrannies.com etc., that you use for logging into your online email account (gmail or whatever it was). The worst thing that could happen is that they get access to your email account, as then they can reset all the passwords on services that are using that email address (including gog.com). After all, then they can easily check your inbox to see all the various services that email is used.
I presume one of the main methods the evildoers work nowadays is that they get hold of the user database in some less secure site (like the aforementioned nudegrannies.com), and then try brute-force to guess the passwords for the various users (email) in that database locally (not trying to repeatedly log into the online service itself as they often limit the failed login attempts, but brute-forcing the user database locally: or decrypt the whole database locally, not sure how they do it... there have been cases where some idiot services haven't even encrypted their user databases so all the usernames and passwords have been in clear text for anyone who gets hold of the user database).
Then they blindly try to use the username+password in various online services and sites, including gmail.com and outlook.com etc., in case the same username+password combination has been used in them.
However in this case they apparently haven't found out your password at least to gog.com, hence the reset password attempt (which is futile if they don't have access to your email).
Naturally, using two-factor authentication wherever you can diminishes the risk of your accounts being hijacked even further, as then it doesn't even matter anymore that much even if they guess your password. So enabling 2FA on your main email account is also highly recommended, but failing that, a long and hard password for your email account that you use nowhere else, and maybe also change from time to time.
(I know the common recommendation is never to use the same password for different online services, but considering people might have dozens or more throwaway online accounts which they've used only once, I guess the reality is something else. People probably don't care even if their online account in some trash site that they've visited only once gets hijacked, as long as money is not used on that site and the same username+password doesn't work on any important sites.)
EDIT: Also if you ever bump into some online service which doesn't use https but http, don't log into such services (or do anything where you type in any sensitive data into them, like your CC number or anything) as all the data you type in goes over the internet not encrypted, including your username and password. Modern browsers increasingly warn of sites not using https.
However not going overboard there, if it is just some generic web site where you just read some text, then it probably doesn't matter that much to you even if it is just plain http...