For anyone not familiar with the character names, the woman seated in panels 1 and 3 is Ms (Rose) Trellis, the CEO at Fastrack, and the younger goth-ish woman standing is Dethany (Dendrobia), one of her key assistants.
Remote play in chess is of course a very real thing, and has been carried out employing the communication channels of any era, going right back to post cards and beyond. So use of SMS-texting or other contemporary chat options for exchange of chess moves is not really a surprise, or a joke. What, then, is?
Later: Arthur has contributed another copy of the image, possibly higher def. Thanks!
And one other. sigh.
Aannnd one more for the old college try:
Comics I Don't Understand 