Lagging when gaming.

This is a long time coming for me, i haven't had the time to do so before but i decided to finally try to resolve this issue.

i bought a new desktop around a year ago or so hoping i'll be able to do more serious gaming, nothing too expensive but supposedly quite good,
and turns out it did improve my gaming considerably, but i noticed that games that have higher requirements do not run well at all despite when i check on websites like canyourunit, i should be able to run it fluidly and that does not appear to be the case, not trying to run 60FPS Dark souls 3 or anything similar.

I am not an expert or anything on this matter so feel free to bring up even trivial tips or questions that may help me to start gaming ^^.

for example: Shiness: Lightning Kingdom, checking on canyourunit my PC should be able to run it pretty easily yet when i start the game i'm lagging so very much.

my PC hardware:
Processor: Intel(R) Core(TM) i5-4460
CPU @ 3.20GHz 3.20 GHz
RAM: 16GB
Windows 10 Pro 64
GPU Intel(R) HD Graphics 4600

forgot to mention, i don't know if it matters in any way but my screen is a TV connected via HDMI cable, an old pilot TV.

here's a small gratitude token for the helpers or forum crawlers xd.

Edit: it seems like my graphics card is the issue from what everyone is saying here, do you have a recommendation for a graphics card?
something that would fit into my system and wouldn't break my wallet completely(i am a student).

Edit2: i am a fucking freaking idiot....
i opened up my PC and it turns out i do have a dedicated GPU(i started doing some research to see the difference between dedicated integrated prices and such)... turns out i wasn't connected properly inside my PC by the store given to me, i reconnected the plugs, switched my HDMI socket inside, i am now connected to a GTX 960 and my gaming runs fucking smooth fluid, over 2 years i've been suffering only because it wasn't connected to the proper place(i had the socket the whole time but trying to connect it before didn't work so i figured it's not supposed to go there).

closing the thread thanks for helping out everyone, without your help i wouldn't have realized it.