Can I use other brand laptop chargers instead of my macbook pro adapter?
Let's start off by addressing the video you linked to....
It's a video by Louis Rossman of The Rossman Group the owner of a laptop repair facility that specializes in component level repair (repairing logic boards).  In it, he explains why he uses a bench top power supply to deliver exactly 18.5V; so he can monitor the amperage draw.  Suffice to say, it's not a &quot;wall wart&quot; he is using.
The MagSafe Adapter.
The MagSafe power adapter can supply voltages from 14.5V to 20VDC.  However, it's not the &quot;brick&quot; that determines if it can charge or not, it's the actual MagSafe adapter that actually determines whether or not it will interface with your Mac.  The brick just supplies the power.
The connector end is what communicates with your laptop and tells the brick how much power to supply.  Basically, the way it works is that it that it identifies the power supply as having so much capacity (wattage).  If it's enough, it will charge/power the laptop.  If not, it won't accept the voltage.
This is why you could use a 90W adapter on a Mac that came with a 40W but couldn't use a 40W adapter on a Mac that needed a 90W.  This is true with all other power supplies except Apple added some logic into their connector.
Is it safe to Use a 3rd party power supply?
If you know what you're doing, then yes, it is.
Will the 18.5V, 6.5A charger work?
It should because it's supplying 120 watts of power (18.5V * 6.5A = 120W; more than enough to satisfy any Mac.
TL;DR
Yes, based on the info you supplied that power adapter will work.  Whether it's safe or not depends on your skills with DC power supplies and electrical circuits.