You're right, the first form is not correct. However the second form also has a problem, because of the pluralisation of "eggs" vs "that of".
To make the second one correct it would need to be something like:
"Unlike the eggs of other fish, those of anchovies are not spherical but are about twice as long as they are wide."
You might go one step further:
"Unlike the eggs of other fish, those of anchovies are not spherical but are *instead* about twice as long as they are wide."
You could correct the first one correct with:
"Unlike the eggs of other fish, anchovy eggs are not spherical but are about twice as long as they are wide." [Here anchovy refers to the animal as a species, so is singular]
or:
"Unlike the eggs of other fish, anchovies' eggs are not spherical but are about twice as long as they are wide."
[Here 'anchovies' refers to anchovies as animals in the world rather than as an abstract species, and the eggs belong to them (plural) - note the possesive apostrophe on the plural form of anchovy]
Hope that helps :)