Do you like this 3 year old step-daughter? If so, then YOU need to be the influence in her life. I don't mean to sound rude, but to me, your husband sounds like a typical "man". You didn't say that he acted differently with YOUR child (more time or interaction) than his own, so at least it's "equal."
If the child is a pain or you don't care for the child or it's a bother, then do something about it. If not, then accept that YOU are going to be the person she connects with and so on.
Remember this too: until my daughter was about 5 or 6, my husband just didn't "get" her...never did anything either.
On Sundays, my husband lays on the couch watching football....and always has no matter what (didn't attend a family funeral because of FB, won't leave the house...except to go watch FB..., won't do any housework or yardwork because of FB...) I am a FB widow on Sunday and after 15 years just accept it and do my own things with my kids...by the way I have 5...and if I'd waited for HIM to be involved with the kids, we wouldn't have any involvement.
The thing I can recommend (around FB games) is family outings....going to a zoo, park, out to eat, to a recreation place....even something like chuckie cheese....do that on an afternoon (Sunday) after or before FB and just say to him, "c'mon, we are going to...blah blah..." and then he can come or not.
If he chooses not to come, at least YOU HAVE MADE memories with YOUR daughter and step-daughter.
One of my best friends was in your similar situation....was married for about 10 years then divorced. She raised her step-daughter (everything you are saying from bathing, to teaching her about "woman" things...mom refused, from how to do her hair to shopping, to everything.....) she was a teen when they divorced and at her wedding a few years ago, STILL referred to her as "Mom".
Isn't the true goal to make an impact with your step-child? Or is it to give your husband a lesson?
One thing I've learned...once a FB addict (couch all day Sunday) ALWAYS a FB addict. Sounds like the real issue is YOUR time with him, doesn't it?
Good Luck!