[Mark / Ohio]

Looks like some smoke when it tries to start. Might try to spray some carb cleaner into the intake and see if it takes off for a sec or two longer. If it does then that goes back to the carb again. If not then maybe it has weak spark.

Did you set/confirm the proper gap on the new plug? Is the plug wet with gas if you pull it out after it sputters and stalls?

 

[Mark / Ohio]

...I pulled out the spark plug after trying to start it and yes, it is slightly wet with gas. I'm guessing this is not a good thing? (I'm a real novice with engines).

Neither good nor bad. Just gives a clue as to what might be going on.

Since the plug is "slightly wet" that means gas is getting into the carb and from there into the cylinder. (That is a good thing. ) But is also leads to the question of why it is not getting burned. It could be the gas is coming from the carb with too rich of an air/fuel mixture flooding the engine. But I'm still kind of leaning toward (guessing) a weak spark as the problem. Next I would check the spark to make sure it is bright blue and strong. It's not totally out of the realm of the possible to have a bad plug right out of the box. It's happened more then once to me replacing plugs in my cars over the years.

Couple links that might be helpful for you:

You can probably find the engine service manual here that would include troubleshooting information:

Manuals | Customer Support | Briggs & Stratton

Here they give troubleshooting tips and how to resolve different issues:

What would prevent an engine from starting? | Frequently Asked Questions | Customer Support | Briggs & Stratton

 

[Mark / Ohio]

From that video looks like the fuel mixture is too rich with the continuing smoke. When you looked at the plug, did it only have gas on it? Or was there also oil on it?