"1E feel" is quite simply the nostalgic feeling that was evoked by the defining characteristics of the first edition: The bare-bones room descriptions for the DM's eyes only; there was almost no pre-written flavor text, unlike what accompanied so many of the late first and most 2nd edition modules. It was the feel of modules, rather than campaign settings.
The Orcus (Clark Petersen) Quote is the best description - it is hard to quantify, and can be best seen rather than described.
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In another light,
Someone on another webiste once said: "In the beginnings of D&D, you had people trading stories like "In my dungeon I have a room where..."; now, people trade stories like "In my campaign I have a town where..." There was more emphasis on setups and challenges of logic rather than situations and challenges of character.
Have you ever noticed how most reminiscences of Players are flavored by their play style or when they started playing? Whereas some stories start with "My favorite game moment was when I rolled a critical success on my jump check and then critically hit and killed the Ogre that was threatening the party", others start with "My fvorite gaming moment was when I talked the Duke of Tristram into not going to war with our home country."
Both are valid, but one gamer's fun is another gamer's boring, and there is a large untapped market of former players out there that remember the "Beer and Pretzels" style of gaming with fondness.