脉 here is read mò (not mài). In this reduplicated 脉脉, it means 'silently expressing feelings through look or gesture' — the medical reading mài (pulse/vein) is wrong here.
history
The 脉脉 sense appears in Xin Qiji's Song-dynasty ci 《摸鱼儿》: 脉脉此情谁诉 ('to whom can I silently confess this feeling?').
