have you thought of possibly going to counselling? this is only going to get worse if you leave it, as i am sure your aware of.
my sister inlaw was in the same situation pretty much as you. her husband would get up early, play video games, go to work, come home, pop right back onto the computer to play video games till 2 or 3am and do it all over the next day. she had 2 children with him and he was no help at all. and she got fed up and depressed over all the responsibility being on her shoulders and it got to the point where she asked her doctor to give her some pills to calm the anxiety. and hid that from her husband, then she got really fed up one day and laid everything on the table, and after that they fought, then decided they were going to start fresh from that point on, he started helping, played his video games less and she stopped taking the pills. and they are very happy with each other.
sometimes you need a fight like that to wake up a little.
it really sounds like a professional has to step in and get to the route of this problem. there has to be a reason why he is obsessed with this...maybe he misses having a full time job, or does not know what to do with himself because he is semi retired.
maybe the fact of working at home is giving him cabin fever, hes bored..
but of course this is not a reason to not shower more than once a week and brush his teeth 2 times a week.
has he always been like this?
maybe try talking to him about why he is constantly playing video games, there has to be a reason. ask him if hes missing something from his life, does he have some friends? maybe ask if he wants to have a guys night, to get him out and back into civilization.
im sure him making dinner would be a huge help on your end because you sometimes work very long hours, maybe you could ask him to make or order something for dinner 3 times out of the week, and just straighten up a little too...and shower more often, and maybe if he sees that after hes fresh and clean you want to be around him more often, maybe hes feeling neglected too and that could be why your sexual life is unsuccessful at the moment or why he makes excuses.
he still has to be able to do what he wants..but he has to think of other people too because there are two people who are important in this situation here, you and himself.
but he cannot always be focused on himself. there has to be a good balance between both.
and if he is still too big headed to try and make a difference in your relationship, maybe he is not worth your time or effort.
and maybe its time to move on.
i hope that was a little helpful.
and wish you the best of luck.