Think about how much time you actually spent 'playing' with your own parents... Maybe you are lucky and had a lot, but I think most of our generation of parents didn't feel the pressure to be their child's constant playmate like we do now. (I'm not saying we 'should' be like out parents - but we can take a leaf out of their book) kids demand attention doesn't mean they should always have it. In fact I personally think it's dangerous for them to have too much, cause they never learn frustration tolerance nor the ability to manage their own time and full it with things they enjoy. I don't think attention equates with love or attachment or anything else. Like everything it's about teaching kids balance - learning when it's appropriate to seek attention and entertainment from caregivers as well as knowing when to enjoy the alone time or seek the attention elsewhere.
I'm quite sure you are doing an awesome job, they will always demand more. So decide what you feel is appropriate and try and stick to it.
Maybe even making Saturday night or afternoon "games night" or something and playing board games etc with them. They don't have to have 1:1 time for it to be quality. As long as you are engaged and actively interested in the activity you do with them - that is much better than just playing with the thing they want you to and barely enjoying it. Let's be honest here - kids play is boring.... I think it is anyway.... and there's nothing anywhere that says being a good parent means playing with kids in a kids way. In fact you will be better just watching and talking with them about what they are doing - rather than actually playing, cause as you said earlier.... You'll always get the play "wrong". Lol.
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