I have a Lenovo Think Centre Edge 72 small and want to move it into a larger case. Read comments for specs/details

It has an intel i7-3770S
Crucial 8GB Kit (2 x 4GB) DDR3L-1600 UDIMM
TP-LINK TL-WDN4800 N900 Dual Band Wireless PCI Express Adapter
and a new 1tb hard drive with windows 10 pro on
MSI NVIDIA GeForce GTX 1050 Ti 4GT LP

Do I need to buy a new mother board and move the pc over or would simply unscrewing all the components work?

Putting the whole thing into a new case will be more then likely impossible… Reason… Where the video card will exit the case… Where all the jacks will exit the case…

Is the list of parts as shown already running in the system? If they are, it is highly advised that you are at the highest possible gaming performance your system will be, except possible HDD to SSD and possibly swapping ram to 2x8GB, that won't change gaming very much.
It is probable the 180 watt TFX power supply is good enough for what you show.

The problem with branded PCs in SFF is that so much may be custom.
Lenovo, or even similar from other companies, becomes a giant list of unknowns.

The motherboard is probably custom mounting. You can measure mounting hole locations versus mini-ITX locations and see if they match up.
The power supply could have custom connections to the motherboard or front panel or both.
The power supply says TFX as size, but that is not a fixed exact dimension.
A carefully chosen used quad core i5 minitower with blogs showing standard parts is far easier for upgrading.
That cpu is an underclock low power i7.
Core i7-3770 @ 3.40GHz score 9309
Core i7-3770S @ 3.10GHz score 8875
https://www.cpubenchmark.net/...u_list.php
http://www.cpu-world.com/Compare_CPUs/Intel_CM8063701211600,Intel_CM8063701211900/

The reason you can't get answers is that nobody knows.