Downloading video is done from within the browser. You can initiate a download by using the 'actions' dropdowns:
For a single-game download, use the 'actions' dropdown to the far right of the game's playlist title: 
... and select the 'download' option:
To download multiple games, use the 'Actions' button along the upper right corner of the page: 
Select the games you want to download by clicking in the small boxes to the left of the playlist titles, click on the 'Actions' button, and select the 'download' option:
If you're downloading multiple files, a pop-up window prepares all of the files into a single zip file.
Please make sure the pop-up window is not being blocked.
Always allow pop-ups from VidSwap. You can disable your pop-up blocker to get your download going:
Now retry the download. The following window will show as your download prepares. This may take a few minutes if there are a lot of files.
Once the download is ready, you'll see the download button to click.
Once it downloads, you can open a zip file on a Mac by simply double clicking on the zip file. It should open for you automatically.
To open zip files on a PC, please follow these steps here.