How the list of 'I Have' games should looks like

Sounds like a lot of work. People with large lists might not want to use such a feature. I can see the appeal though.

That is right about the hard work on this for large list. though i have see large list where people had already put the steam store link for each of their game, they may like such a feature.

Of course it will be a lot of work to do if you have to put many games, but on the other hand if I knew that someone has such list I would like to see that and see in easy way which games I dont have.
And of course if someone doesn't want to use this method, he may use old method.
And there is no big programming work because the tool is already done in giveaways. This is only use the same tool in second place.
I hope steamgifts team will be interested of that.

I imagine it even could be easier, if you don't have another list where you copy from, since you only have to type a few characters and it then gives you possible games containing the sequence. So you can click on it. Also it would make searching for particular games a lot more reliable. So there is a certain incentive to do the initial work.