You seem to already have a knack for the strategy aspect so working on your micro I think will go a long way to improving your play.
Another thing that'll help is learning to judge engagements. If you don't think you're going to win a fight it's usually best to retreat and save your manpower. There were a lot of engagements in that game where you had single Grenadier squads fighting two enemy squads at once. Never be afraid to retreat if you don't think a fight is in your favour.
Also remember to use the Attack Move command. It'll tell your units to stop and shoot if they see any enemies, usually at their maximum range where engagements are quite slow.
It's not as good as manually your units into cover, but it's better than them blindly walking into enemy fire while you're not looking and is very helpful when you've got a lot to do at once.
If you haven't seen them already, Tightrope's Starter Series and Micro Tips and Tricks series are very good.
https://www.youtube.com/watch?v=fkDhwSaDOBA&list=PLMJFmZl8aYOeoRdddMg7im6dwJHI4y7bL
https://www.youtube.com/watch?v=2rkp3LLM3WA&list=PLMJFmZl8aYOdW4tzX-S3VL2tq5JfuiViK