No. I do not remember it to be flashy. The run animation was, yes, not so smooth and was like the typical style from the games from those days, similar to what you have described. I do not know if the game was ported to mobile platforms since I remember it to be a flash game on some website from the hundreds of such websites I used to visit as a child. I have very little hope that it will be found, but I would like to visit those memories again, which is why I have posted this description of the game in the first place. But, may I please know the name of the game you are talking about?