Hi, this is not a technical answer but this is how I understand it as a native speaker.
We say ‘i am going to my friend’ or ‘i am writing to my friend’ as this implies time must pass for the letter to travel to them or for me to physically get to them in person.
Texting is instant so their is no physical travel, be that a letter or me personally and no passing of time.
So when we say ‘i am texting’ we do not need to say to, it is already understood.
I hope this does not confuse you even more and is of some help.
I am sure a professional teacher can explain this in a technical way but hopefully two different ways of explaining might be most helpful :)