I won't claim to know what is causing your elbow pain, but I did notice that you are short stroking many of your reps(not to full lockout) and you are not flaring your elbows at the top of the lift. This will cheat your lockout strength out of good work. If the pain only comes on close grip benching maybe the stroke length isn't the problem. Shortening the stroke with the use of a board defeats the purpose of increasing speed off the chest. I usually vary my grip on speed days from close, to medium, to wide. Maybe just limiting the close grip sets would help.
"I can't wait 'til tomorrow, 'cause I get stronger every day!"