The short and simple answer is no, you do not need to have permissions of 777 (world-writable) to use SnippetMaster.
In fact, I do not recommend putting your files to permission of 777.
The long and complicated answer is that the permissions needed are 100% dependent on your web hosting server configuration. In other words, the required permissions to "write" to a file you are trying to edit has nothing to do with the SnippetMaster software itself.
It totally depends on your web hosting provider, and how they have configured any PHP software (such as SnippetMaste) to "run" on their servers.
If your hosting provider has configured PHP software to run as the "nobody" apache web server user.. then you will need to give permission of 777 to your files if you want them to be writable/editable by PHP software (such as SnippetMaster). This is insecure, and you should find a different hosting provider that does things differently. Period.
You should use a good hosting provider that runs PHP using "cgi mode". This means that all PHP software (SnippetMaster) runs on the web server as your actual website account user, instead of with the "nobody" user.. so that you don't have to give world-write permissions of 777 to the files you want your PHP software (SnippetMaster) to be able to edit.
Any good hosting provider should run PHP like this (using "cgi mode"). Most don't because it is easier to run PHP using "nobody" user.. and also takes less resources (cpu/memory, etc), so the host can put more accounts on their server to make more profit.
It is more expensive to run a web server with PHP using the more secure "cgi mode", which is why such accounts cost more... the advantage is that you don't need to give "777" permissions to your files and security is much better.
If you'd like a referral to a good hosting provider (where PHP is run using "cgi mode") and where you can get free SnippetMaster PRO licenses (rebrandable version), please let me know.
Also, please feel free to post a reply here if you have any questions about Snippetmaster security or file permission requirements.