Yep there are cursive traditions for writing Chinese characters, and there is historically quite a bit of acceptable variation on how you write the characters (

Yep there are cursive traditions for writing Chinese characters, and there is historically quite a bit of acceptable variation on how you write the characters (think lowercase 'a' or 'g' in Latin). Just like with Latin script ability to read cursive is also fading as people handwrite less; the computer/print forms you see come from the woodblock forms/Ming typeface and there's a large stylistic shift going from brush writing to woodblock forms.