Is there an algorithm for factoring N, which is just as simple as this one, but faster?
Pure nonsense. For choosing the random $\Delta$ between $\sqrt{\min(N, Ň)}$ and $\sqrt{\max(N, Ň)}$ there are too many possibilities for it to work. For example whenever the first and last digits of $N$ differ, you get something like $\frac{1}{10} \cdot \sqrt N$ possibilities (the exact formula doesn't matter).

So you can replace the first formula $\gcd[N, (k × Ň) + Δ]$ with $k=1$ by this one: $\gcd[N, \Delta]$. Try all $\Delta$ between $1$ and $\sqrt N$, the number of possibilities is within some small factor.

Compared to the division, computing $\gcd(N, x)$ has the advantage that at each attempt you try all factors of $x$. This is good in case $N$ has some small factors, which in case of RSA is surely not true.

I see no advantage of the linked algorithm to trial division. Trying all primes up to $\sqrt N$ is probably faster, terminates also when $N$ is prime, and has a bounded time.

Summary: pure nonsense.