The answer to where snag-it stores videos while recording varies on the version of Snag-it you are using. For version 12 it is more complicated than for Vversion 11: you have to click on the tri bar on the floating Snag-it button (which usually resides at the top of your screen), and then select 'Manage Profiles'. The another window opens up and at the top under 'Capture Profiles' you need to select either 'Image' or 'video', depending on which capture type you want to setup. Both are setup the same way. So, if you are looking to setup the folder you want the captured videos to go to, then make sure you highlight 'video'. Then you need to make sure both 'Region' and 'File' are set in the boxes below.
If 'File' is not already set in the box, then click on the down arrow in the 'Share:' box, and select File. Then click on the start to the immediate right and another window pops up. Here is where you set the file naming convention to be used in making the file names, AND the folder name where the saved video capture will go. Make sure 'Always use this folder:' is clicked and the click on the manila envelop icon and walk thru your file system to the desired folder. If you do not have a folder already created, you can create it here thru this technique, but I would suggest always creating your folders first.
With Version 11 it is a lot easier: click on the Snag-it floating icon and select 'Open the classic capture window'. Notice on the lower right of this window that there is a big red circle, and to the left of it are three choices: image, text, video. So, if you are looking to set the video capture folder, then click on 'video'. 'File' needs to be the selection under the word 'Share', and if it is not, then click on the down arrow (just like in Version 12) and select 'File'. Once 'File' is set in this box, then click on the down arrow and now select 'Properties'. This will bring you to the same window as described above for Version 12 where you set the file naming convention AND the capture folder.
Version 13 may be different as well, but I quite using Version 12 because it is so user unfriendly, so I never paid for version 13, assuming it would be terrible as well. Hence, I know nothing about version 13.