As @erinnnn mentioned, on-demand mobile access is available only for Premium users.
However, it's available on selected playlists for Free users as well, there will be no shuffle symbol next to the title of the playlist. That means, you can choose a song you want to play and you have unlimited skips.
Most of the playlists from Made For You section are not limited.
You can still play on-demand using a desktop, even without Premium Subscription.
Here's an article comparing different Subscriptions offered by Spotify. Take a look if you're interested.
I hope you'll find this helpful!
Emilia_8Rock Star 10
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