Still it feels a bit unclear what iy means to be "eliminated at the same time". It could suggest being slow in the placement is an advantage; we play it saying it ends if all players are "eliminated in the same turn". My guess is this was the intended rule.
Also "Players look at their cards, find the matching pieces and place them one at a time." I guess (but am not sure) "one at a time" refers only to placement, right? (I mean you look at all the cards, you find all the matching pieces THEN you place them in the order you like.)
Don't overthink it or try to metagame it by moving slower than others.
Simultaneous play - playing 1 piece at a time