I think that explanation is only about Hydrogen molecules and hydrogen atoms, not Hydrogen vs. Helium.

There's a free textbook available here [1] that explains that atomic sizes decrease across the periodic table and increase down. In short, it decreases across a horizontal period because more electrons are in the same orbital shell (really a cloud), increasing the negative nuclear charge of the cloud, which is more attractive to the positive atomic nucleus, so the whole cloud is squeezed together, making the whole atom smaller.

[1]: https://chem.libretexts.org/Bookshelves/General_Chemistry/Bo...