Would this fit into my case?

Dimensions-wise you are ok. The heatsink will fit the case.

You also need to check the height of the RAM modules and make sure they will not create an interference in slot #1. Tall RAM heat spreaders are usually a problem. Check this out. I did notice that the heatsink specified is narrower than other heatsinks, but taking some measurements on the motherboard and checking the them against the dimensions of the heatsink will be more positive.

Also checkout clearances should you decide to install side fans inside the case.