This is a really good question with some other good information here, so let me try to deconstruct some assumptions here that may not be accurate but results from somewhat confusing information.
The short answer is that a tabs violation has no effect on insurance premiums, although your ticket is properly marked traffic (read on to see why). Not everyone gets their renewal letter - it's your obligation to keep the tabs current, but sometimes mail doesn't get delivered and sometimes the DOL has the wrong address. State law expects you to notice when your tabs are expired and to renew them, regardless of whether you get a courtesy reminder.
Now, for the long answer. A civil infraction is a noncriminal offense for which the penalty is a monetary fine, but no jail time.
There are two kinds of civil infractions in the State of Washington - traffic, and nontraffic. When you think "traffic," think traffic or motor vehicle code, as opposed to nontraffic, which might be consuming an alcoholic beverage in a city park, to give just one example.
Traffic and nontraffic do NOT mean moving and nonmoving. So why is a ticket marked traffic if the offense is a tabs violation? Because a tabs violation is under the motor vehicle code. Moving and nonmoving (which is not marked on the ticket) is something that most lawyers know, but it's not required that the cops tell people which offenses affect insurance and which do not. There are violations marked "traffic" that are nonmoving, and ones that moving. It really depends on the offense(s).
What are the other differences?
1. Traffic means that failing to respond can result in a license suspension; nontraffic means that failing to respond is a crime (this is spelled out on the ticket you received);
2. The State keeps this information for statistical purposes in gathering information about how many infractions involve traffic laws (most infractions) and how many do not (nontraffic such as parks, or fish and game violations).
3. People's rights. See #1 above. The penalties for failing to respond to a notice of NONTRAFFIC infraction is higher as it can include jail.