var arr = [
[1, 2, 3, 4, 5, 6, 7],
[4, 3, 2, 55],
["", "", "", ""]
];
const mustStay = arr => arr.some(n => n !== '');
const newArr = arr.filter(mustStay);
arr.reduceRight((_, n, i, a) => mustStay(n) || a.splice(i, 1), null);
// или
arr.splice(0, arr.length, ...arr.filter(mustStay));
// или
let numDeleted = 0;
for (const [ i, n ] of arr.entries()) {
arr[i - numDeleted] = n;
numDeleted += !mustStay(n);
}
arr.length -= numDeleted;