I think you could switch them off in your options. If not you could just tell your e-mail that chess.com is "junk mail" and everything from chess.com would go to the junk mail section in your inbox...
"You're about to lose on time" e-mails

Account / Online Chess Settings / (scroll down) Uncheck "alert me when it is my move, I am running out of time, or I receive a challenge"

Usually your email client will allow to send things to Spam ("junk mail") based on a matching subject line, rather than everything from chess.com. That seems to me to be the most precise solution.

But I use the chess.com mail. So I can't make chess.com as spam, and these e-mails are even more pointless (as when I log onto chess.com, I first play in games close to timing out, later check my e-mail).

But I would like to get other notifications.
You already receive those notifications on your messages and alert panels on your home page (except the "about to time out" alerts)... do you really think you need them into your email too? (more over if you are using the chess.com email)

But you would continue receiving those, even when you unchecked that alert.
(it is only about online chess games)

EMAIL SETTINGS
Also send alerts to my default contact@chess.com email address.
(In most cases, you will only receive 1 email per login.)
It's OK to email me about Chess.com news and announcements.
(You will NEVER receive 3rd party email or non-Chess.com email.)
Looks like I had that off already. So it's something else.

If you're using chess.com's e-mail as the recipient for these then aren't you required to log into chess.com before checking it? It seems to me that having e-mail turned on at all becomes entirely redundant with the alerts you've chosen to receive when you're set up this way. Can't you turn the e-mails off altogether and simply rely on the chess.com Alerts to give you the notification's you're interested in?
I can agree that the control over alerts and e-mails could be more granular and user friendly, but it seems like there's a simple solution to your complaint.

On the bright yellow corner on your top-right corner, click on change alerts. Then, deselectthe options about emailing you, about anything. this should do the trick.

Also send alerts to my default contact@chess.com email address.
(In most cases, you will only receive 1 email per login.)
It's OK to email me about Chess.com news and announcements.
(You will NEVER receive 3rd party email or non-Chess.com email.)
Looks like I had that off already. So it's something else.
Hmmm, as do I -- I stand corrected. It looks like there may be no way to turn these alerts off.

About the only way to beat Kacparov right now would be on time, or maybe bribe his parents to force him to go outside and play. You rule, CM!

If you know the subject line you should be able to configure your email client to push these emails straight to your deleted items bin if you are using an email client like MS Outlook.

Also send alerts to my default contact@chess.com email address.
(In most cases, you will only receive 1 email per login.)
It's OK to email me about Chess.com news and announcements.
(You will NEVER receive 3rd party email or non-Chess.com email.)
Looks like I had that off already. So it's something else.
That one is not the same I proposed to you. Look at the following route:
HOME\Account\Online Chess Settings\
http://www.chess.com/home/echess_settings.html
Game Alert Preferences
alert me when it is my move, I am running out of time, or I receive a challenge.
play a sound when it is my move.
(Uncheck the first one)
I have recently started a lot of 1 day games. Because of school I can only play in the afternoons. So every time I go on in the afternoon, I get like 20 e-mails saying I'm about to lose in time because I have less than 8 hours left. I know that very well, and I have antitimeout protection (just in case something happens). Is there a way of switching those e-mails off (or getting only 1, not 20)?