I spent over 20 years in video games publishing....
As Paul says, the games you buy in the shops are licensed only for home use (in the same way that DVD/Blue Ray movies are). You can't legally rent them out or use them for other commercial use such as rentals or hosting an outdoor cinema.
Back when video rental stores were a thing they had to buy a much more expensive rental version of a VHS/DVD/Blue Ray. Valve software (creators of Half-Life, Team Fortress and the Steam gaming platform) also used to have a page on their website about licensing game for commercial use in Internet/gaming cafes. I can't find that page any more so maybe they no longer offer rental licensing.
Conclusion
You would need to contact the publishers of the games to see if they offer rental licensing versions of their games. I have been out of the industry for some time but my feeling is that most won't be interested. They are too invested into digital sales and streaming now.
Renting out games without the correct license would be a breach of copyright and you could be sued. What is worse it is not like a speeding ticket.... you don't just get a single, fixed fine for the one instance. They look back at how long you have been doing it, how many games etc and they levy bigger fines for the more serious infringements. They can even ask you to account for all profits made and have that as a penalty instead.