hi weeys,
Employee engagement activities are usually social in nature.
It envolves all those activities which allow the employees to interact with each other and play some games or just pass time discussing non office topics.
This helps them to fulfill their social needs and is a great motivator for them.
In our office we celebrate all the birthdays of our employees on the 15th of each month. We order food and cake for everyone and their is a patry on that day.
We also celebrate major festivals as ethinic day or with some special dress codes.
I guess, it can be said that all the social activities done in and for the office are largely covered under employee engagement. However social activities have a much larger spectrum than employee engagement.