At 16 months he's not supposed to be able to do much with his hands yet. They are still moving their hands by moving their shoulders and elbows. Later comes moving the hand by moving the wrist and finally they start being able to have much better fine motor skills in their hands then eventually their fingers.
If you notice most kids when they color, they hold the crayon in a grip then they use their whole arm to move the hand, as they get older the ability to move the crayon gradually moves down the muscles in their arm. As your child gets older he's going to develop those better skills to play the games better.
It truly sounds like you might need to download a couple of new games.
It might also be that he's still healing inside. I'd be concerned about his interest in playing the body part game. That's usually when they have mom's or dad's complete attention and play enthusiastically. They get that one on one time and play hard.
Here's a link to Parent Center. If you put in his name and birth date, age, etc...they send you a weekly, monthly email of what he should be doing and what to expect to see next. It might help you to know that all kids do develop differently.
For instance, some kids never crawl, they go directly from rocking on their hands and knees to walking. They eventually have to go back and learn to crawl because crawling is part of some needed skill they have to have to progress to another stage later on. It's all about how these skills are rewiring their brain.
http://www.parentcenter.com/toddler.html