The short answer is that it's totally up to the website to intentionally obscure data entered in any field with •••• or **** or whatever. The decision to code the website in that manner is completely unrelated to its encryption or transmission protocol. Strictly speaking it's not even necessary to echo any characters, but such an apparent lack of response to user input would be confusing and run counter to fundamental human interface guidelines.
Whether that practice enhances overall data security or not is debatable. Clearly if someone or some thing is looking over your shoulder as you are typing a social security number or other sensitive data it's probably a good idea to obscure what you're typing. But if that someone or something is going to go through such trouble it's not much more difficult to look at what your fingers are doing instead. Personally I think it's my problem to be aware of my surroundings — a personal responsibility I don't delegate to technology.
Going further down that rabbit hole, it is theoretically possible for some sensitive equipment to remotely pick up the faint electromagnetic radiation emitted by the display you're looking at, and use that signal to recreate the images on it without any kind of visual, optical, or physical means. If a website echoes •••• characters, that's all that can be determined from what gets drawn on the screen. That's the argument in favor of obscuring information, but it is entirely unrelated to the data being transmitted to and from the website. That had been the purpose of the "lock" icon — to show the website is using encryption, which nearly all of them do now.
Not all websites use encryption; for example a website that neither contains nor solicits anything that can possibly be considered sensitive information would not require it.
However, even my favorite such page uses encryption:
<html>
<head>
<title>Blank White Page</title>
</head>
<body BGCOLOR="white" TEXT="black">
<BASEFONT SIZE=3 FACE="Arial" >
<div id="popup" style="position:absolute;top:0;left:0;"></div>
</BODY>
</html>
😄