What you’re seeing is probably just a different font that looks more like handwriting than printed characters. The hiragana in the PDF look very legible to me (better than my own handwriting!).
But to answer your thread title, yes stroke order in Japanese (whether for kana or especially kanji) is very important. The stroke order has evolved over time to make writing the characters more fluid and come out natural-looking.
I can basically read hiragana letters at very natural speed at this point and I never bothered learning the stroke orders. I wasn’t worrying about writing when I learned them. It isn’t necessary.