I’m not sure what their company/aircraft SOP’s are but in a Windshear Go-Around on the 777 (where it shouts Windshear, Windshear with a red warning on the ND) you DO NOT change config!
You apply TOGA thrust, ensure the speedbrake is stowed (windshear is only active below 1500’ agl hence you might be using the brake or have it auto armed) and fly the flight directors. No flap change and certainly no gear change! The reason being that aerodynamically you might need the flaps if the microburst/windshear loses you massive amounts of airspeed. Hence leave it where it is!
The gear is another interesting one. Few people realise quite how much drag the main gear and nose gear doors produce (not sure about the 737 as I’ve never flown it!). Hence our SOP is to leave the gear down as the transient drag might be too much for TOGA power to be able to give you sufficient speed during the event.
Get the warning, apply TOGA thrust, check speed brake, fly through the event (windshear events often have 2 stages, entry and exit). Once you and your colleague have determined that the event is over and stable flight has been resumed, call ‘go-around, flaps XX’, ‘Positive rate’, ‘Gear Up’ and climb away.
Had it a fair few times. Properly handled it is a non event.
Edited to add, just watched the video and it seems that is exactly how it was handled. Nicely done.
The reason the skipper seems to get grumpy is that he was manually flying and probably coming out of the event with TOGA power on (you can hear the hail hitting the windscreen as they pass through). That will cause the jet to accelerate very quickly indeed hence he’s calling for the flap, doesn’t get it, and is probably rapidly approaching flap and gear overspeed! The FO was probably overloaded and not responding. In an overload situation the first sense that goes is hearing!