For those of you who don't know, the Game & Watch handhelds were a series of LCD handhelds released prior to the Gameboy that featured one (and sometimes two) player games. Some of these games (like Donkey Kong II or Mario's Cement Factory). Other games, however, all featured the same looking character, who later got the name Mr. Game & Watch in Masahiro Sakurai's Super Smash Bros. series. My question is if there were ever any hints during this era that suggested that Mr. Game & Watch was an original, recurring character.
The character of Mr Game and Watch was created by Makato Kano. In an "Iwata Asks" interview from April 2010, Satoru Iwata describes him as being
... involved with every aspect of design, from the character known as Mr. Game & Watch to the exterior box.
A later section discussed the design of the LCD graphics:
Iwata: After an idea came together, what was the next step?
Kano: After we all brainstormed and the basic situation of the game had been determined, Yokoi-san would say, "The rest is up to you." (laughs)
Izushi: By "you," he meant Kano-san. (laughs) Kano-san would redraw our clumsy drawings on the black board, and then it would look really interesting and we'd say, "Let's do it!"
Elsewhere in the interview, they discuss the use of an LCD driver designed for a calculator. This could drive 72 display segments. (In a calculator these would be similar shapes grouped together to display digits, but the LCD could be manufactured with segments of different shapes and sizes.)
Displaying a four-digit score counter (and also watch) used several of these segments, leaving roughly 44 available for displaying all the game elements. For a moving character, that includes all the positions the character can be in. To save on segment use, the character would best be drawn with a single contiguous segment.
The interview includes several photos of Kano's artwork for the LCD displays. They have a similar style, which is unsurprising given that they were all drawn by one person. As the games were released on a monthly basis, there would have been little time to explore different visual styles.
In what is a fairly wide-ranging interview, there is no mention of Mr. Game and Watch being an intentionally recurring character.
Given the limitations of the technology used, and the fact that a single artist drew all the LCD designs, I think it's reasonable to conclude that the similarity between the characters in the Game and Watch games was a natural occurrence, as opposed to an intentional choice to have a recurring character.