It is basically that. New Yorkers have a lot of colloquialisms and have a relaxed way of referring to things sometimes, and one of those is referring to WABC as "Channel 7", especially for the older generations, they identify ABC 7 as "Channel 7" not sure how much longer people will continue to say "Channel 7" since these days we don't "tune" channels anymore everything is digital so perhaps in the near future, I wouldn't be suprised if they returned back to rebranding their newscast as "ABC 7" Eyewitness News especially since their online presence is now "ABC 7" NY. to me it makes more sense to identify as "ABC 7" again. There is an old thread over in the New York Forum here that discussed the branding switch when it happened in 2004 (20 years ago now, wow does the time fly). Most of us came to the consensus at the time that the switch was made because the average New Yorker identified Channel 7 with the newscast. I don't think they are mandated to say "Channel 7" ocassionally reporters say "ABC 7".
Another thing that WABC and the other O&Os abandoned that KABC and KGO in the north retain is the iconic "Circle 7" Pins. Every KABC and KGO on-air staffer wears it, WABC and WLS had that standard for a while, especially in the early days but dropped it I guess in the early 90s. Personally I like them, and since WABC is the top in the nation, it would be a nice honorary symbol for them.