I bought this board with 2 attiny's. Can I program with this? I can't get it's COM port to show up.
What's on the underside of that board? Nothing?
It looks to me like a socketed digispark board, meaning you would need an attiny85 bootloaded as a digispark to program it in place (and you'd need to add a reset button too, as far as I can tell - IIRC you need to do a hardware reset on the digispark to start the bootloader), or you could use it to supply power from a micro USB port to an already programmed attiny x5 or 13.
I think you bought the wrong thing - if you want to program an attiny with cheap things from ebay/aliexpress, get a USBAsp (or USBTinyISP) clone. Note that neither of these show up as a COM port.