Oh what the heck I'll get in on this one . I'll agree that engine doesn't sound good but it should do better than that regardless of a bad clutch ,ignition problem or a bad carb. The saw started on the second pull unless it was previously warmed up for the video. If the saw had an ignition timing problem it would show up before it fired and be hard to start. The carb kind of sounds like the high speed side is lacking or plugged up, restricted in some way.
Something is binding and holding back the chain speed. See what happens without the bar and chain. I'd start there and work backwards. Other than the chain brake being engaged how about the nose sprocket in the tip of the bar being half way seized or clogged with dirt and sawdust. The bar rails clogged with sawdust and dirt or overly tight due to mismatched chain and bar combo or worse and rare is wrong chain pitch and drive sprocket combo or a slightly bent bar.