thephotostick app will not open after I pulled out the memory stick

Couple of things in that screenshot:

1. Is the app only 1kb? Really?
2. It's not on your Mac but actually on iCloud, so there's no way it will run from there.

So, insert the gadget and copy the app to your Applications folder, then try launch it. It's so old it's unlikely to work, but that's your best shot.

You can't update it if it hasn't been updated by the makers in 7 years. Maybe to time to find an alternative.

I'm not familiar with that app; however, I checked their website and since there is nothing to install, you do need the stick to be plugged in if you want to work with it. I am also leary of software that has not been updated since Mac OS 10.7 and saw some accounts that the failure rate was one in three.

So, bottom line: it is a third party device/app, so you need to contact their support.