COPI/COPII proteins and kinesins/dyneins
Interesting question. The term anterograde refers to movement in the forward direction. In the context of vesicular trafficking, anterograde refers to (1) movement from the site of protein synthesis in the rough endoplasmic reticulum (RER) towards the Golgi and then (2) movement from the Golgi towards the final destination in the cell.

Both processes rely on microtubules for transport. Microtubules are polar and radiate from the microtubule organizing center (MTOC) with their (+) ends directed towards the periphery of the cell:



There are two broad classes of molecular motors that facilitate directed movement along microtubules. Kinesins are generally (+)-end directed motors whereas dyneins are (-)-end directed:



These images should already give you a hint. Your question may have arisen due to the assumption that the ER is centrally located near the MTOC with the Golgi somewhat peripheral. This is incorrect. In reality, the Golgi complex is actively clustered near the MTOC by movement on microtubules. Furthermore, the ER extends along the microtubule network towards the (+)-end periphery. Taken together, it is evident that microtubule (-)-ends are located near the Golgi and transport to it from any part of the cell, including the RER, requires the (-)-end directed motor dynein. Subsequent anterograde transport from the Golgi to a specific destination in the cell, or through the secretory pathway, requires the (+)-end directed motor kinesin. Retrograde transport from the Golgi back to the ER would also use kinesin: 





The article cited in the question (which I also reference in this answer), mentions that COPII vesicles are coupled to microtubules via dynactin. Dynactin is a protein complex that is used to both activate and adapt cargo to dynein (ie COPII vesicles are coupled to microtubules via a dynein/dynactin complex):