Yes, both devices need to have the ShareIt application installed because it's using its own proprietary protocol in order to send and receive files.
This is what I've extracted from the official website:
I have SHAREit running, but others cannot connect. Why?
Please make sure:
1. You both have SHAREit launched and running on your devices;
2. You have selected different roles, that is, one of you is a sender, and the other is a receiver;
3. Both devices have their wireless radios turned on.
At the point 1, you see that ShareIt needs to be on the same devices, therefore answering your question.