Not sure if your aware but Visio files are considered restricted and you are forced to download before it can be opened in the client application (Including Visio viewer). This of course is very annoying, you could deal with this in these manners
1.Install Office Online Server and connect SharePoint (New-SPWopiBinding) then set your Document Library to 'Open in Browser', please see this article for more information on these steps.
2.Set the visio application to being permissive by running the following PowerShell commands
$webApp = Get-SPWebApplication <WebAppUrl>
1.Change from Classic Experience to New Experience and set Document Library to use 'Open in Browser'
P.S. For extra bonus points, any file type that your being forced to download but want to just open from SharePoint can be set to 'Permissive' in this same manner see here for mime types. But make the change at your own risk as some file types really should not be opened directly from SharePoint due to security concerns.