So I've been looking at the numbers we have. In 2019 the Switch was ~400k from being a majority of units (obviously legacy systems exist but at this point they are very small). Up until October the PS4 and XBO are at ~3.2 million. Let's says for Nov/Dec they move 400k (based on their shipments I feel this may be even optimistic if anything). Let's say the PS5/XSX sold 1300k/900k in Nov (this is basically the upper limit for both). Finally, they both somehow sell 1300k in Dec. Add that up and you get about 8.4 million. We know through Nov the Switch is at ~6.9 million (tad higher actually). So the Switch needs to only sell about 1.5 million to be a majority of units.
Looking in the past, post NES, 1998 seems the only plausible year where a system (this case the PS1) was a majority of units sold. Granted the 90's numbers out there aren't exact, and NPD makes revisions, but it's very possible the PS1 did so. So this could be a very notable year in that regard.
If you widen the net to a hardware maker having a majority of units, then Nintendo 1999, 2000, 2003, 2004, 2007-2010, and maybe 2019 (depending on how much 3DW did that year) could qualify. And again, probably Sony 1998 too.
Alternatively, if you only want to look at home consoles, then definitely PS1 1998, probably PS1 1999, PS2 2002, and 2005 qualify.
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