We only support the browsers listed in the specs below:
That said, the NPAPI plug-in is installed in a central location and should be available for use system-wide. It's very likely that you will need to use Firefox to install the NPAPI Flash Player in the future. If you don't want to deal with the hassle, you might consider switching to a browser that includes Flash Player as a built-in component, like Internet Explorer on Windows 8 and higher, or Google Chrome.
The site (I'm assuming you're referring to get.adobe.com/flashplayer) is assuming Maxthon is Chrome-based browser because the site uses the UserAgent string information to determine the browser in use. Maxthon identifies itself as various browsers in the UserAgent string and the first one after Matxthon is Chrome, which explains why the site thinks it's Chrome. You can use the link kglad posted to get the NPAPI plug-in, or you can go to get.adobe.com/flashplayer/otherversions and select your OS version and then select 'Flash Player for Other Browsers'. Both options will install the NPAPI plug-in on your system.
Thank you all for the help.