I think that's fairly normal growth habit. I have at least a dozen Aglaonema plants and a couple of them seem to want to trail. All of mine are indoors except one Silver Bay plant that stays outside but it seems to want to trail too. A couple of it's stems have adventitious roots forming and I'm sure if they ever reach the soil, they will take anchor.
'Chocolate'
'Dud Unyamanee' (center plant with stems trailing out of the pot.)
'Silver Bay', the pot was laying on it's side during the hurricane and I haven't had a chance to clean it up yet.
'Silver Bay' adventitious roots.
I find Aglaonema stems will root very easily. Last year my 'Pink Dalmatian' plant was getting very tall and lanky so I chopped it off and stuck the cut stems down in an old terrarium to root. This is the mama plant today.
These are 'Pink Dalmatian' cuttings in the old terrarium that I still haven't potted up; they are now bigger than the mama plant.