I do not spend the entire day playing with my daughter (also 4) - some days more than others, but not all the time. I need to get other things done, and she needs to learn to be able to entertain herself. Being able to self-entertain is a valuable skill, but it needs to be taught. I think the issue on Supernanny sometimes is you have people who don't get down and play with their kids and spend quality time with them at all, or expect the TV to always entertain them and be an electronic babysitter.
I would try upping the amount of time you do spend on average - maybe shoot for 20 to 30 minutes of playtime, then tell her you have to do XYZ now. You can try setting a timer for the amount of time that she will be expected to entertain herself, say 30 minutes, then you will play a game with her, whatever. Make sure she does have things that she can entertain herself with - my daughter does have coloring books, crayons, paper, play-doh, toy sets, sticker books, etc. that don't really require me to get directly involved. I will play some things with my daughter (like board games and card games) and other things I do tell her she needs to play with her friends because the truth is, I'm just not that into it (like hide-and-seek and tag).
If she starts to whine and cry, discipline her for it. I tell my daughter all the time if she is going to carry on like that because she does not like what I am telling her, she can go do it in her room, because I am not going to listen to it. She is not to go following me around, being a pest and sticking her pouty face into my face, begging for attention.
I know it's hard, and I have struggled with the same guilty feelings, but I do think it's a balance that we have to find. Sometimes spending quality time with your kids and giving them happy memories of a mom that played with them needs to be more important than how clean the house is. But they also need to understand that you are not their constant playmate and the dishes and the laundry are not going to do themselves. It doesn't take that much time to load the dishwasher or fold up some laundry, and then go back to playing a game with your kids - and the kids can learn to be patient and wait for Mom to be ready to spend one-on-one time with them. I think in some ways it is harder when you have an only child (like mine) instead of a couple of siblings to entertain each other. But siblings sometimes mean bickering and arguments that have to be broken up too.