Possible reason 1.

RiftGG, while opening, is trying to access to one folder and has no permission to do so. Please, try to open RiftGG as administrator. 

Possible reason 2.

The antivirus you have installed in your computer is blocking RiftGG for any reason. Please, try to deactivate the antivirus and open RiftGG. In this case, you might have to white list RiftGG to be able to use it. 

Possible reason 3.

If you had RiftGG installed previously and it was since you installed the last update that it crashed, could be that you have a conflict with old db. Create a copy in your desktop, and delete it from RiftGG folder. Then restart the software. If this process solves the problem, there is a conflict with you db folder. Send it to support@rift.gg and will attend you as soon as possible

If none of this work, send the crash logs support@rift.gg and will attend you as soon as possible.