Nolan Bushnell and Ted Dabney were probably the first people to actually start buildign a coin-op video game (or at least the first anyone knows about) but who was the first to think of the idea? (and I'm talking serious consideration here - like someone who was serio.us about doing it)
Let's look at a few contenders.
This is probably the answer most would give. Nolan claims that he first saw Spacewar at the University of Utah. Varying accounts date this incident from as early as 1962 to the "mid-60s" and claim that Bushnell thought of monetizing the game either soon after seeing it, or while working at the Lagoon Amusement Park during this same period.
But is this account true? Ted Dabney claims that Bushnell never mentioned Spacewar (or the idea of a commerial video game) to him until he saw the game at Stanford around 1969. Of course, just because he didn't mention the game to Dabney doesn't mean he hadn't seen it earlier, but there is still some question regarding the accuracy of his account of having seen the game as an undergrad. IIRC, Goldberg and Vendel wonder if Bushnell claimed to have seen it in the mid-60s in order to establish priority over Ralph Baer (who started working on his video game in 1966). They also pointedly (again, IIRC) omit any mention of Nolan seeing the game at U of U. I did a quick search to see if I could verify that University of Utah did have the game by the mid-1960s, or even if they had a PDP-1 by then (since DEC supposedly included the game on all the units they sold) but didn't really find anything. Of course, even if he did see the game in the mid-60s, that doesn't mean he saw the dollar signs at that time.
So, if Nolan didn't come up with the idea until 1969-ish (and I'm not saying that is or isn't the case - his account may be entirely truthful), who might have done so earlier?
Steve Russell et al
At least one source I read mentioned that the Spacewar design team briefly discussed the idea of trying to sell the game but quickly dropped it, figuring that DEC was their only potential customer and they wouldn't be interested. Even if this is true, however, it doesn't really count because a) it sounds like it was nothing more than a brief discussion rather than a serious proposal and b) it wasn't for a coin-op version of the game.
According to Galaxy Game designer Bill Pitts, Hugh Tuck was the one who suggested creating a coin-op version of Spacewar. But when did this occur? Pitts said he saw the game around two years after he enrolled at Stanford in his Junior year. Pitts enrolled in 1964 so that would place the incident around 1966 or 1967. He also says that he realized Tuck's idea was feasible about three years later when he was working for Lockheed and saw that DEC had released the PDP-11. The PDP-11 was released in December, 1970 but I don't know when Pitts found out about it. The two of them formed Computer Recreations in June of 1971, however. From this info, Tuck's suggestion of monetizing the game came somewhere between 1966 and 1968.
According to the Wikipedia entry for Nutting Associates, engineer Richard Ball drew up a proposal for a coin-op video game called Space Command. After Nutting passed on the idea, Ball and coworker Ransom White formed their own company called Cointronics. There are some problems with this story, however. First, the Wikipedia article is completely unsourced. In 2012, someone named Judith Guerin left a comment on an article by Benj Edwards about Computer Space that made essentially the same claim, but again no source is given and I don't know who Judith Guerin is. I don't know if she was using Wikipedia as her source or vice versa or if they both used a different source.
Even if the story is true, however, when did it occur? A Google books search revelas that Cointronics showed two games (Zap Ball and Ball/Walk) at the 1968 MOA show so they were around by then. A search of the California Secretary of State website shows that Cointronics incorporated in early 1969 so it seems to be a good guess that the company was formed sometime in 1968 and Ball left Nutting shortly before. I was unable to track down Ball or White (though I did confirm that White usually went by "G. Ransom White"). So let's say this incident occured in 1968.
Unknown Stanford Student/Staffer
FInally, there's this video:
This is from a 2006 panel discussion that was part of a celebration of the PDP-1. The panel included a number of members of MIT's famed hacker community of the 1960s, including Alan Kotok, John McCarthy, Peter Sampson, and Spacewar creator Steve Russell. During a q-and-a session after the discussion, an unidentified audience member claims that in 1966 or 1967 American Express provided Stanford with seed money for a program to come up with potential projects for future development. The person claims he drew up a proposal to put a multi-player version of Spacewar on a dedicated, timeshared PDP-1, put it in a bowling alley or shopping center, and charge people to play. Stanford considered the idea too frivolous to submit.
Unfortunately, I have no idea who this guy is. I don't think it's Hugh Tuck (plus, his story is very different from Tucks) but if his story is true, he might be a good candidate. True, his game likely wouldn't have had a coin-slot, since it seems he was talking about charging per block of time, but he was thinking about putting the game in a bowling alley.
Of course, ideas are cheap and there could well have been any number of people who entertained the idea of a coin-op "video" game far earlier than any of those mentioned above (and some would say that it's irrelevant who thought of the idea - it's who implemented it that matters).
Odds and ends
Speaking of Computer Space, here's an early article on the game from the May, 1972 issue of Vending Times
And speaking of Nolan Bushnell, take a look at this:
So who is that and what does he have to do with Nolan Bushnell?
That's John Bushnell, Nolan's great-grandfather. Born in England in 1823, John came to America and went to Utah in 1850 in one of the early companies of Mormon settlers. At one point, he actually wanted to return home but Brigham Young sent him to the new town of Fillmore, where his family was one of the first six in the area. He opened a store and a post office before trading his property for a farm in nearby Meadow in 1862.
OK, that really doesn't have anything to do with video games, but I found it interesting.
Finally, speaking of Cointronics, here's a photo of their countertop game Ball/Walk (games like this drive me nuts since I suck at pretty much any game other than pinball that involves a steel ball - I tried to play Ice Cold Beer once and I think I got one ball in hole).