Yes, you're exactly right. Here you have two equality checks, which have the same operator precedence. First one evaluates first, then its result applies to the next equality check.
1===1===1
is the same as (1===1)===1
which is true===1
which is false
, because here you check by values AND their types. 1==1==1
will result in true
, because it checks equality by values only, so 1==1==1
equal to (1==1)==1
equal to true==1
equal to true
.