I've been laminating cabs for over 10-years. It s great surface to apply side art to or to even make a nice side. I prep the cab suraface with a belt sander with 36-50 grit to make fast work. Make sure you take off any loose surface material and ensure the edges are chip free as mentioned above. Th trimmer will follow whatever you leave for an edge.
Wilsonart is good stuff for the adhesive and laminate. I use the Red like HFK mentions but I am fairly certain its 600 (can is in the garage and im not there

) I use a spray gun and spray it on. A brush is such a mess and you will use 10x as much needed. I've had the same spray gun for over 10 years. I just leave the glue in it all the time. I've gone 3 months or more in between spraying and filling it up, sometimes more.
I've never used dowels, but that is a good idea. I pick a factory end and side of the laminate after I have rough cut it to the cabinet size (rectangle) Usually 6' x 30" or so. Measure cab adn add a few inches to length and width, usually 3-4.
I start at the bottom of the cab with the edge in hand and the rest of the sheet flipped over my head (get a visual). I carefull line the bottom edge up with the back edge (because they are square) and slowly roll the sheet up. Press firmly then use the "J" roller pictured above then trim out. I also use a smooth file on the finished cab to hit the edge so that its not sharp.
Now, there are 3 types/grades of laminate. horizontal, vertical and shelf liner. For games, shelf liner is best because you can still use 3/4" t-mold no problem. Shelf liner is super thin but brittle.
With the vertical grade, I lay into the edge of the cab a little with the belt sander during prep so 3/4" t mold fits nice. Horizontal grade is pretty thick and not recommended for the side unless you get some 13/16's t-mold. Most home stores carry horizontal.