What would be a good substitute for the arrowroot in this recipe? Thanks!

Pegeen's answer is spot on. Corn starch can also be used as a direct substitute for arrowroot!

The arrowroot is used as a thickener, since mushrooms give off a lot of water and in this recipe are also mixed with other liquids. If you don't have arrowroot, try 1 Tablespoon flour whisked hard with with 1 Tablespoon water. After stirring in, let things simmer for a minute to cook down.