Yes, a guy that has sustained eye contact with you and lingers when he touches you is flirting with you. He is doing all of that with the intent of getting you to reciprocate. It is important that you do. A lot of girls make the mistake of shying away from reciprocating when a guy is making flirtatious gestures at them.
The thing is, by doing this, you are risking him taking this to mean that you aren’t interested in him. A guy wants to know that the woman he is flirting with is into him.
Should he get the impression that you aren’t, on account of a lack of reciprocation, he loses interest in you and moves on. So, be sure to reciprocate the next time he flirts with you. This sends the message to him that you are interested, which encourages him to ask you out on a date in the foreseeable future.