Gaming laptops can be bought at good value these days but their real advantages are unused if you just leave them always at the desk. If you only want to declutter your desktop, I suggest to either:
1) just upgrade the gpu and if needed the psu (if the current psu is to weak or if you get power failures, often good psu's gold or above certified have a lifetime of 7 or more years and factory assurance of 5-7 years) and place the desktop somewhere on the ground.
2) buy a mini-itx case (around ~30-75 bucks) and either find a motherboard that supports your current cpu or buy also a new cpu & motherboard (AMD newest Ryzen cpu's are good bang for buck now) and buy a new gpu (e.g. rx 570 / 580 or 1060 / 1070 gtx) and possible psu (see first point).
Gaming laptops main disadvantage in my opinion is that with most (gaming) laptops when one part breaks or if you want to upgrade, you sometimes have to replace other parts too or even buy a whole new laptop. While mini-itx desktops are a good middle approach (with almost all the advantages of a full desktop tower) and can be more budget friendly too.