3 minutes late is not a big deal. The first session is honestly more like a get to know you session and to figure out where he is performing at (even if there was testing done prior since kids change). Computers can be used in therapy as a motivator as well as to play speech based games. Did this therapist come recommended to you? I get that you are anxious about getting your money's worth and your son succeeding. I would try a few sessions before pulling the plug.

Give them a few sessions before you decide.

I can't comment on the therapist being late, you'll have to see if that's a pattern. She's a person too.

If she saw that he was thirsty and needed water to clear his throat and be able to speak than that's important. Make sure that he's well hydrated.

What you see as playing a game is therapy. Speech therapy consists largely of articulation games, games for relaxing muscles, and games to promote speech sounds. A lot of these can be computerized. A good speech therapist uses a variety of games and tools including classic children's toys. The session will look like play instead of work.

If you have questions about goals and what is being done during the session, ask. Ask how she intends to measure progress.

My child just started Speech and Language Therapy today.
Mostly for articulation and written language issues.
The therapist arrived 3min late to the office. Took a couple more minute to settle in,
offered my son water which invoved going to another part if the center. It seem like half of
the session was on a computer playing some sort of game.
I guess I am venting about investing time and money
into this and worrying it won't be with it.
She want to see him 2xs a week for 45min.
Thoughts?