What it means is this:
Some types of heavy armour have a Str requirement. If you don't meet the requirement, your speed drops by 10. But as an exception, dwarves are entitled to ignore this Str requirement. They don't suffer that speed penalty even if they don't meet the Str requirement. This is special exception, just for dwarves. Even low-Str dwarves can wear heavy armour and not be slowed down.
If you use the variant encumbrance rules, though, you ignore the Str requirement for heavy armour anyway. So you can also ignore the exception that exempts dwarves from it because everyone is now exempt. You work out the encumbrance for everyone the same way, dwarves and non-dwarves alike, based on all-up weight of equipment vs Str.
Using the variant encumbrance rules makes it tougher for all the PCs, which is presumably what you want, to make the game more challenging. It makes it especially tougher for low-Str dwarves wanting to wear heavy armour because now they have to abide by the same rules as non-dwarves even though their base speed is lower (but no worse than a halfling).