Those will be OK for games pre 2010.
http://www.tomshardware.com/forum/387463-33-intel-4000-geforce-620m gives the not to the 620.
Do not fall for benchmarks showing the Intel being OK. It's not and is so bad I will not discuss this further.
Well, I can’t afford any expensive laptops but I have doubts about two types of laptops. The first one is an Acer with Intel core I5, 6gb ram and a integrated HD graphics 4000. The second one is also an Acer... but, with a intel core I3, 4gb ram and a HD graphics 620. My doubt is, I want to play some games but nothing heavy as you already noticed that both laptops can’t do much, so, the first one or the second?