"Psychological - A Genre of story where characters face problems that are psychologically haunting. Commonly seen in thriller or suspense stories".
"Tomodachi Game" follows a group of 5 friends who one day have found themselves in a white room and were forced to play a debt repayment game with multiple rounds/levels. The only way to win this game is to "Trust Your Friends". If not, something unthinkable happens and it's not just the crippling debt.
A good psychological Anime explore the mental state of a said character when thrown in a scenario where they have to endure a lot of mental damage like Stress/Anxiety/Fear/Depression etc. Tomodachi Game does this but very poorly. It's a death game that is as basic and generic as possible. Yuuichi, the OP protagonist everyone knows about; Kokorogi the typical big-rack damsel in distress who loves the MC; Shiho, the bossy 'strong' girl character who lasted only for 6 episodes who's supposedly crazy in the head; Shibe, the typical goof with a lot of head weight; and Tenji, by far the only decent character in the entire show. This Anime suffers from, what I like to call an "Ugly Face Syndrome". They throw in an ugly face of a said character to show how mentally fucked up the characters are, which brings the shock value and creates tension. This isn't exactly a bad thing, some of my favorite Anime (Mononoke & Kaiji, for example) use the same trick but they succeed in doing so, because they let you perceive the inner conflict of the said character but Tomodachi Game fails to achieve this. It just shows this bunch of over-the-top characters 'evil' plans with exaggerated facial expressions and it's just nothing but a pure shock value because it carries no weight when you haven't established the inner conflict or given any solid reason to care for these characters. Tenji is the only one who had something of a character flashback which fleshed out his character a bit and made him into a decent character.
TL;DR
Basic & generic characters with no proper characterization makes for a poorly written psychological show. It's no different from an edgy death game Anime, except we have ugly faces instead of gore.
The MC antics might carry the show tho.
Is it full of flaws? Yes.
So, it's not entertaining? No. It IS entertaining. If you're here for entertainment, then the Anime is covered like many.
Cocky characters who exist to crushed by the MC, sexy female characters who ready yo fawn over him, a plot with ridiculously high stakes only for our MC to break with simple logic, a catchy opening and an OP MC with just the right amount of mystery surrounding his past with a believable weakness, atleast makes "Tomodachi Game" an entertaining Anime.