Here is another, somewhat similar approach
First, make sure your expectations are realistic. Evaluate whether naptime needs to be reduced or the time changed. Do you need to be waking them up earlier, either in the morning or at naptime? In other words, is your child ready for sleep at the times you are putting them down? Is there anything else disrupting their sleep cycle (such as being in a room with a computer or tv screen right before bedtime, having a bath too close to bedtime, teething, illness, etc.)
Then, assuming that you have ruled out reasons that would make it impossible for this child to sleep at this time, here is what I did. After the bedtime routine, I put my child in bed, spent a minute or two singing a song or two or just talking soothingly. With my son we developed a routine of me saying certain phrases, then he repeats them. "Good night. I love you. Have a good sleep. See you in the morning." At 4.5 years old this is still our goodnight routine. With my current 2 year old DD I hold my face right next to hers, giving 'nose kisses' and she puts her hand on my arm. She seems to just need that moment of closeness.
Then I turned around and sat on the floor beside the bed, with my back to the child. No more talking, no more contact. In the summertime I would read a book (enough light from the window), in the winter I hid my phone down low and checked my email. Anything so I'm not just sitting there being impatient. Otherwise I'd have trouble staying calm. If the child attempted to get out of bed, I calmly lay them back down, with NO TALKING. Usually they didn't try more than a couple of times, because I was right there. Once they were drowsy enough to stay still (usually 10-15 minutes at the beginning), but before they fell asleep, I'd give one more super soft kiss and then leave. They were still awake, so they knew I was leaving, but sleepy enough to not worry about it. It's a fine line, but they need to be able to fall finally asleep alone. If you stay until they are completely asleep, they expect that everytime. I think if they are not getting to 'drowsy' in a reasonably short time, then you need to move back to step one- evaluate why they are not sleepy.
After a few days, once the child stopped trying to get up, I'd move halfway across the room and wait there. Then a few more days, moved to the doorway, then to the hallway, then to my room (right across the hall.) Anytime the child got up, I silently and gently put them back, without making any sounds.
Every child is different, but this worked for my youngest 2. (My first child I didn't do this with and she was much older before she'd stay in bed.