The short answer here is no. The long answer is: maybe, depending on the specs of your Ultrabook and the types of games you want to play. The vast majority of Ultrabooks run on integrated graphics, which means that they perform graphical tasks directly on the CPU with system RAM used as video memory.
Some Ultrabooks do have a discrete GPU with its own dedicated video memory, such as the Dell XPS 15 (2022) at the top of this list. Those Ultrabooks should definitely be able to cope with gaming, but don't expect to be running anything at maximum graphical settings without taking a serious hit to your framerates.
Ultrabooks that don't have a proper GPU (most in this list use Intel's Xe integrated graphics) will generally struggle in games, unless you're only playing 2D indie games or older titles that aren't graphically demanding. If you really want to play the latest games, consider one of the best gaming laptops instead - or a thin and light gaming laptop, if you want to keep a svelte form factor.